KILLED proof of input_MmTFVtUFVW.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).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), 138 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (14) CpxRNTS (15) InliningProof [UPPER BOUND(ID), 458 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), 0 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), 5 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) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtGraphSplitRhsProof [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), 3 ms] (82) CdtProblem (83) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 18 ms] (100) CdtProblem (101) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 35 ms] (104) CdtProblem (105) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 25 ms] (108) CdtProblem (109) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 50 ms] (116) CdtProblem (117) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2 ms] (120) CdtProblem (121) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 51 ms] (128) CdtProblem (129) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms] (130) CdtProblem (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 26 ms] (132) CdtProblem (133) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 9 ms] (134) CdtProblem (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 21 ms] (144) CdtProblem (145) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 25 ms] (148) CdtProblem (149) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 5 ms] (150) CdtProblem (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 16 ms] (152) CdtProblem (153) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (158) CdtProblem (159) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 70 ms] (160) CdtProblem (161) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 4 ms] (162) CdtProblem (163) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13 ms] (164) CdtProblem (165) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (166) CdtProblem (167) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (168) CdtProblem (169) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 5 ms] (170) CdtProblem (171) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 33 ms] (172) CdtProblem (173) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (174) CdtProblem (175) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 39 ms] (176) CdtProblem (177) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (178) CdtProblem (179) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 36 ms] (180) CdtProblem (181) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (182) CdtProblem (183) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 38 ms] (184) CdtProblem (185) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (186) CdtProblem (187) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 25 ms] (188) CdtProblem (189) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 2 ms] (190) CdtProblem (191) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (192) CdtProblem (193) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (194) CdtProblem (195) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 45 ms] (196) CdtProblem (197) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (198) CdtProblem (199) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 47 ms] (200) CdtProblem (201) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (202) CdtProblem (203) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 70 ms] (204) CdtProblem (205) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (206) CdtProblem (207) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 38 ms] (208) CdtProblem (209) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (210) CdtProblem (211) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (212) CdtProblem (213) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 45 ms] (214) CdtProblem (215) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (216) CdtProblem (217) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (218) CdtProblem ---------------------------------------- (0) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__U11(tt, V2) -> a__U12(a__isNat(V2)) a__U12(tt) -> tt a__U21(tt) -> tt a__U31(tt, N) -> mark(N) a__U41(tt, M, N) -> a__U42(a__isNat(N), M, N) a__U42(tt, M, N) -> s(a__plus(mark(N), mark(M))) a__isNat(0) -> tt a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2) a__isNat(s(V1)) -> a__U21(a__isNat(V1)) a__plus(N, 0) -> a__U31(a__isNat(N), N) a__plus(N, s(M)) -> a__U41(a__isNat(M), M, N) mark(U11(X1, X2)) -> a__U11(mark(X1), X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U21(X)) -> a__U21(mark(X)) mark(U31(X1, X2)) -> a__U31(mark(X1), X2) mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(0) -> 0 a__U11(X1, X2) -> U11(X1, X2) a__U12(X) -> U12(X) a__isNat(X) -> isNat(X) a__U21(X) -> U21(X) a__U31(X1, X2) -> U31(X1, X2) a__U41(X1, X2, X3) -> U41(X1, X2, X3) a__U42(X1, X2, X3) -> U42(X1, X2, X3) a__plus(X1, X2) -> plus(X1, X2) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__U11(tt, V2) -> a__U12(a__isNat(V2)) a__U12(tt) -> tt a__U21(tt) -> tt a__U31(tt, N) -> mark(N) a__U41(tt, M, N) -> a__U42(a__isNat(N), M, N) a__U42(tt, M, N) -> s(a__plus(mark(N), mark(M))) a__isNat(0') -> tt a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2) a__isNat(s(V1)) -> a__U21(a__isNat(V1)) a__plus(N, 0') -> a__U31(a__isNat(N), N) a__plus(N, s(M)) -> a__U41(a__isNat(M), M, N) mark(U11(X1, X2)) -> a__U11(mark(X1), X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U21(X)) -> a__U21(mark(X)) mark(U31(X1, X2)) -> a__U31(mark(X1), X2) mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(0') -> 0' a__U11(X1, X2) -> U11(X1, X2) a__U12(X) -> U12(X) a__isNat(X) -> isNat(X) a__U21(X) -> U21(X) a__U31(X1, X2) -> U31(X1, X2) a__U41(X1, X2, X3) -> U41(X1, X2, X3) a__U42(X1, X2, X3) -> U42(X1, X2, X3) a__plus(X1, X2) -> plus(X1, X2) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (3) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (4) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__U11(tt, V2) -> a__U12(a__isNat(V2)) a__U12(tt) -> tt a__U21(tt) -> tt a__U31(tt, N) -> mark(N) a__U41(tt, M, N) -> a__U42(a__isNat(N), M, N) a__U42(tt, M, N) -> s(a__plus(mark(N), mark(M))) a__isNat(0) -> tt a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2) a__isNat(s(V1)) -> a__U21(a__isNat(V1)) a__plus(N, 0) -> a__U31(a__isNat(N), N) a__plus(N, s(M)) -> a__U41(a__isNat(M), M, N) mark(U11(X1, X2)) -> a__U11(mark(X1), X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U21(X)) -> a__U21(mark(X)) mark(U31(X1, X2)) -> a__U31(mark(X1), X2) mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(0) -> 0 a__U11(X1, X2) -> U11(X1, X2) a__U12(X) -> U12(X) a__isNat(X) -> isNat(X) a__U21(X) -> U21(X) a__U31(X1, X2) -> U31(X1, X2) a__U41(X1, X2, X3) -> U41(X1, X2, X3) a__U42(X1, X2, X3) -> U42(X1, X2, X3) a__plus(X1, X2) -> plus(X1, X2) 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, V2) -> a__U12(a__isNat(V2)) [1] a__U12(tt) -> tt [1] a__U21(tt) -> tt [1] a__U31(tt, N) -> mark(N) [1] a__U41(tt, M, N) -> a__U42(a__isNat(N), M, N) [1] a__U42(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1] a__isNat(0) -> tt [1] a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2) [1] a__isNat(s(V1)) -> a__U21(a__isNat(V1)) [1] a__plus(N, 0) -> a__U31(a__isNat(N), N) [1] a__plus(N, s(M)) -> a__U41(a__isNat(M), M, N) [1] mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1] mark(U12(X)) -> a__U12(mark(X)) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(U21(X)) -> a__U21(mark(X)) [1] mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1] mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1] mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] a__U11(X1, X2) -> U11(X1, X2) [1] a__U12(X) -> U12(X) [1] a__isNat(X) -> isNat(X) [1] a__U21(X) -> U21(X) [1] a__U31(X1, X2) -> U31(X1, X2) [1] a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1] a__U42(X1, X2, X3) -> U42(X1, X2, X3) [1] a__plus(X1, X2) -> plus(X1, X2) [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, V2) -> a__U12(a__isNat(V2)) [1] a__U12(tt) -> tt [1] a__U21(tt) -> tt [1] a__U31(tt, N) -> mark(N) [1] a__U41(tt, M, N) -> a__U42(a__isNat(N), M, N) [1] a__U42(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1] a__isNat(0) -> tt [1] a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2) [1] a__isNat(s(V1)) -> a__U21(a__isNat(V1)) [1] a__plus(N, 0) -> a__U31(a__isNat(N), N) [1] a__plus(N, s(M)) -> a__U41(a__isNat(M), M, N) [1] mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1] mark(U12(X)) -> a__U12(mark(X)) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(U21(X)) -> a__U21(mark(X)) [1] mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1] mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1] mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] a__U11(X1, X2) -> U11(X1, X2) [1] a__U12(X) -> U12(X) [1] a__isNat(X) -> isNat(X) [1] a__U21(X) -> U21(X) [1] a__U31(X1, X2) -> U31(X1, X2) [1] a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1] a__U42(X1, X2, X3) -> U42(X1, X2, X3) [1] a__plus(X1, X2) -> plus(X1, X2) [1] The TRS has the following type information: a__U11 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 tt :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 a__U12 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 a__isNat :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 a__U21 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 a__U31 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 mark :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 a__U41 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 a__U42 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 s :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 a__plus :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 0 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 plus :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 U11 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 U12 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 isNat :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 U21 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 U31 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 U41 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 U42 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 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: a__isNat_1 mark_1 a__U21_1 a__U42_3 a__plus_2 a__U41_3 a__U31_2 a__U11_2 a__U12_1 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, V2) -> a__U12(a__isNat(V2)) [1] a__U12(tt) -> tt [1] a__U21(tt) -> tt [1] a__U31(tt, N) -> mark(N) [1] a__U41(tt, M, N) -> a__U42(a__isNat(N), M, N) [1] a__U42(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1] a__isNat(0) -> tt [1] a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2) [1] a__isNat(s(V1)) -> a__U21(a__isNat(V1)) [1] a__plus(N, 0) -> a__U31(a__isNat(N), N) [1] a__plus(N, s(M)) -> a__U41(a__isNat(M), M, N) [1] mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1] mark(U12(X)) -> a__U12(mark(X)) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(U21(X)) -> a__U21(mark(X)) [1] mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1] mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1] mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] a__U11(X1, X2) -> U11(X1, X2) [1] a__U12(X) -> U12(X) [1] a__isNat(X) -> isNat(X) [1] a__U21(X) -> U21(X) [1] a__U31(X1, X2) -> U31(X1, X2) [1] a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1] a__U42(X1, X2, X3) -> U42(X1, X2, X3) [1] a__plus(X1, X2) -> plus(X1, X2) [1] The TRS has the following type information: a__U11 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 tt :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 a__U12 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 a__isNat :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 a__U21 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 a__U31 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 mark :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 a__U41 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 a__U42 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 s :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 a__plus :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 0 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 plus :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 U11 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 U12 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 isNat :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 U21 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 U31 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 U41 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 U42 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 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) -> a__U12(tt) [2] a__U11(tt, plus(V1', V2')) -> a__U12(a__U11(a__isNat(V1'), V2')) [2] a__U11(tt, s(V1'')) -> a__U12(a__U21(a__isNat(V1''))) [2] a__U11(tt, V2) -> a__U12(isNat(V2)) [2] a__U12(tt) -> tt [1] a__U21(tt) -> tt [1] a__U31(tt, N) -> mark(N) [1] a__U41(tt, M, 0) -> a__U42(tt, M, 0) [2] a__U41(tt, M, plus(V11, V2'')) -> a__U42(a__U11(a__isNat(V11), V2''), M, plus(V11, V2'')) [2] a__U41(tt, M, s(V12)) -> a__U42(a__U21(a__isNat(V12)), M, s(V12)) [2] a__U41(tt, M, N) -> a__U42(isNat(N), M, N) [2] a__U42(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1] a__isNat(0) -> tt [1] a__isNat(plus(0, V2)) -> a__U11(tt, V2) [2] a__isNat(plus(plus(V13, V21), V2)) -> a__U11(a__U11(a__isNat(V13), V21), V2) [2] a__isNat(plus(s(V14), V2)) -> a__U11(a__U21(a__isNat(V14)), V2) [2] a__isNat(plus(V1, V2)) -> a__U11(isNat(V1), V2) [2] a__isNat(s(0)) -> a__U21(tt) [2] a__isNat(s(plus(V15, V22))) -> a__U21(a__U11(a__isNat(V15), V22)) [2] a__isNat(s(s(V16))) -> a__U21(a__U21(a__isNat(V16))) [2] a__isNat(s(V1)) -> a__U21(isNat(V1)) [2] a__plus(0, 0) -> a__U31(tt, 0) [2] a__plus(plus(V17, V23), 0) -> a__U31(a__U11(a__isNat(V17), V23), plus(V17, V23)) [2] a__plus(s(V18), 0) -> a__U31(a__U21(a__isNat(V18)), s(V18)) [2] a__plus(N, 0) -> a__U31(isNat(N), N) [2] a__plus(N, s(0)) -> a__U41(tt, 0, N) [2] a__plus(N, s(plus(V19, V24))) -> a__U41(a__U11(a__isNat(V19), V24), plus(V19, V24), N) [2] a__plus(N, s(s(V110))) -> a__U41(a__U21(a__isNat(V110)), s(V110), N) [2] a__plus(N, s(M)) -> a__U41(isNat(M), M, N) [2] mark(U11(U11(X159, X259), X2)) -> a__U11(a__U11(mark(X159), X259), X2) [2] mark(U11(U12(X73), X2)) -> a__U11(a__U12(mark(X73)), X2) [2] mark(U11(isNat(X74), X2)) -> a__U11(a__isNat(X74), X2) [2] mark(U11(U21(X75), X2)) -> a__U11(a__U21(mark(X75)), X2) [2] mark(U11(U31(X160, X260), X2)) -> a__U11(a__U31(mark(X160), X260), X2) [2] mark(U11(U41(X161, X261, X327), X2)) -> a__U11(a__U41(mark(X161), X261, X327), X2) [2] mark(U11(U42(X162, X262, X328), X2)) -> a__U11(a__U42(mark(X162), X262, X328), X2) [2] mark(U11(plus(X163, X263), X2)) -> a__U11(a__plus(mark(X163), mark(X263)), X2) [2] mark(U11(tt, X2)) -> a__U11(tt, X2) [2] mark(U11(s(X76), X2)) -> a__U11(s(mark(X76)), X2) [2] mark(U11(0, X2)) -> a__U11(0, X2) [2] mark(U12(U11(X164, X264))) -> a__U12(a__U11(mark(X164), X264)) [2] mark(U12(U12(X77))) -> a__U12(a__U12(mark(X77))) [2] mark(U12(isNat(X78))) -> a__U12(a__isNat(X78)) [2] mark(U12(U21(X79))) -> a__U12(a__U21(mark(X79))) [2] mark(U12(U31(X165, X265))) -> a__U12(a__U31(mark(X165), X265)) [2] mark(U12(U41(X166, X266, X329))) -> a__U12(a__U41(mark(X166), X266, X329)) [2] mark(U12(U42(X167, X267, X330))) -> a__U12(a__U42(mark(X167), X267, X330)) [2] mark(U12(plus(X168, X268))) -> a__U12(a__plus(mark(X168), mark(X268))) [2] mark(U12(tt)) -> a__U12(tt) [2] mark(U12(s(X80))) -> a__U12(s(mark(X80))) [2] mark(U12(0)) -> a__U12(0) [2] mark(isNat(X)) -> a__isNat(X) [1] mark(U21(U11(X169, X269))) -> a__U21(a__U11(mark(X169), X269)) [2] mark(U21(U12(X81))) -> a__U21(a__U12(mark(X81))) [2] mark(U21(isNat(X82))) -> a__U21(a__isNat(X82)) [2] mark(U21(U21(X83))) -> a__U21(a__U21(mark(X83))) [2] mark(U21(U31(X170, X270))) -> a__U21(a__U31(mark(X170), X270)) [2] mark(U21(U41(X171, X271, X331))) -> a__U21(a__U41(mark(X171), X271, X331)) [2] mark(U21(U42(X172, X272, X332))) -> a__U21(a__U42(mark(X172), X272, X332)) [2] mark(U21(plus(X173, X273))) -> a__U21(a__plus(mark(X173), mark(X273))) [2] mark(U21(tt)) -> a__U21(tt) [2] mark(U21(s(X84))) -> a__U21(s(mark(X84))) [2] mark(U21(0)) -> a__U21(0) [2] mark(U31(U11(X174, X274), X2)) -> a__U31(a__U11(mark(X174), X274), X2) [2] mark(U31(U12(X85), X2)) -> a__U31(a__U12(mark(X85)), X2) [2] mark(U31(isNat(X86), X2)) -> a__U31(a__isNat(X86), X2) [2] mark(U31(U21(X87), X2)) -> a__U31(a__U21(mark(X87)), X2) [2] mark(U31(U31(X175, X275), X2)) -> a__U31(a__U31(mark(X175), X275), X2) [2] mark(U31(U41(X176, X276, X333), X2)) -> a__U31(a__U41(mark(X176), X276, X333), X2) [2] mark(U31(U42(X177, X277, X334), X2)) -> a__U31(a__U42(mark(X177), X277, X334), X2) [2] mark(U31(plus(X178, X278), X2)) -> a__U31(a__plus(mark(X178), mark(X278)), X2) [2] mark(U31(tt, X2)) -> a__U31(tt, X2) [2] mark(U31(s(X88), X2)) -> a__U31(s(mark(X88)), X2) [2] mark(U31(0, X2)) -> a__U31(0, X2) [2] mark(U41(U11(X179, X279), X2, X3)) -> a__U41(a__U11(mark(X179), X279), X2, X3) [2] mark(U41(U12(X89), X2, X3)) -> a__U41(a__U12(mark(X89)), X2, X3) [2] mark(U41(isNat(X90), X2, X3)) -> a__U41(a__isNat(X90), X2, X3) [2] mark(U41(U21(X91), X2, X3)) -> a__U41(a__U21(mark(X91)), X2, X3) [2] mark(U41(U31(X180, X280), X2, X3)) -> a__U41(a__U31(mark(X180), X280), X2, X3) [2] mark(U41(U41(X181, X281, X335), X2, X3)) -> a__U41(a__U41(mark(X181), X281, X335), X2, X3) [2] mark(U41(U42(X182, X282, X336), X2, X3)) -> a__U41(a__U42(mark(X182), X282, X336), X2, X3) [2] mark(U41(plus(X183, X283), X2, X3)) -> a__U41(a__plus(mark(X183), mark(X283)), X2, X3) [2] mark(U41(tt, X2, X3)) -> a__U41(tt, X2, X3) [2] mark(U41(s(X92), X2, X3)) -> a__U41(s(mark(X92)), X2, X3) [2] mark(U41(0, X2, X3)) -> a__U41(0, X2, X3) [2] mark(U42(U11(X184, X284), X2, X3)) -> a__U42(a__U11(mark(X184), X284), X2, X3) [2] mark(U42(U12(X93), X2, X3)) -> a__U42(a__U12(mark(X93)), X2, X3) [2] mark(U42(isNat(X94), X2, X3)) -> a__U42(a__isNat(X94), X2, X3) [2] mark(U42(U21(X95), X2, X3)) -> a__U42(a__U21(mark(X95)), X2, X3) [2] mark(U42(U31(X185, X285), X2, X3)) -> a__U42(a__U31(mark(X185), X285), X2, X3) [2] mark(U42(U41(X186, X286, X337), X2, X3)) -> a__U42(a__U41(mark(X186), X286, X337), X2, X3) [2] mark(U42(U42(X187, X287, X338), X2, X3)) -> a__U42(a__U42(mark(X187), X287, X338), X2, X3) [2] mark(U42(plus(X188, X288), X2, X3)) -> a__U42(a__plus(mark(X188), mark(X288)), X2, X3) [2] mark(U42(tt, X2, X3)) -> a__U42(tt, X2, X3) [2] mark(U42(s(X96), X2, X3)) -> a__U42(s(mark(X96)), X2, X3) [2] mark(U42(0, X2, X3)) -> a__U42(0, X2, X3) [2] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] a__U11(X1, X2) -> U11(X1, X2) [1] a__U12(X) -> U12(X) [1] a__isNat(X) -> isNat(X) [1] a__U21(X) -> U21(X) [1] a__U31(X1, X2) -> U31(X1, X2) [1] a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1] a__U42(X1, X2, X3) -> U42(X1, X2, X3) [1] a__plus(X1, X2) -> plus(X1, X2) [1] The TRS has the following type information: a__U11 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 tt :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 a__U12 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 a__isNat :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 a__U21 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 a__U31 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 mark :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 a__U41 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 a__U42 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 s :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 a__plus :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 0 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 plus :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 U11 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 U12 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 isNat :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 U21 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 U31 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 U41 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 U42 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 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') -{ 2 }-> a__U12(a__U21(a__isNat(V1''))) :|: V1'' >= 0, z = 1, z' = 1 + V1'' a__U11(z, z') -{ 2 }-> a__U12(a__U11(a__isNat(V1'), V2')) :|: z = 1, z' = 1 + V1' + V2', V2' >= 0, V1' >= 0 a__U11(z, z') -{ 2 }-> a__U12(1) :|: z = 1, z' = 0 a__U11(z, z') -{ 2 }-> a__U12(1 + V2) :|: z' = V2, z = 1, V2 >= 0 a__U11(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U12(z) -{ 1 }-> 1 :|: z = 1 a__U12(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U21(z) -{ 1 }-> 1 :|: z = 1 a__U21(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U31(z, z') -{ 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'') -{ 2 }-> a__U42(a__U21(a__isNat(V12)), M, 1 + V12) :|: z' = M, z = 1, z'' = 1 + V12, V12 >= 0, M >= 0 a__U41(z, z', z'') -{ 2 }-> a__U42(a__U11(a__isNat(V11), V2''), M, 1 + V11 + V2'') :|: z' = M, V11 >= 0, V2'' >= 0, z = 1, z'' = 1 + V11 + V2'', M >= 0 a__U41(z, z', z'') -{ 2 }-> a__U42(1, M, 0) :|: z'' = 0, z' = M, z = 1, M >= 0 a__U41(z, z', z'') -{ 2 }-> a__U42(1 + N, M, N) :|: 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__U42(z, z', z'') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U42(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__isNat(z) -{ 2 }-> a__U21(a__U21(a__isNat(V16))) :|: z = 1 + (1 + V16), V16 >= 0 a__isNat(z) -{ 2 }-> a__U21(a__U11(a__isNat(V15), V22)) :|: z = 1 + (1 + V15 + V22), V22 >= 0, V15 >= 0 a__isNat(z) -{ 2 }-> a__U21(1) :|: z = 1 + 0 a__isNat(z) -{ 2 }-> a__U21(1 + V1) :|: z = 1 + V1, V1 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__U21(a__isNat(V14)), V2) :|: V14 >= 0, z = 1 + (1 + V14) + V2, V2 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__U11(a__isNat(V13), V21), V2) :|: V21 >= 0, V13 >= 0, V2 >= 0, z = 1 + (1 + V13 + V21) + V2 a__isNat(z) -{ 2 }-> a__U11(1, V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNat(z) -{ 2 }-> a__U11(1 + V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNat(z) -{ 1 }-> 1 :|: z = 0 a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__plus(z, z') -{ 2 }-> a__U41(a__U21(a__isNat(V110)), 1 + V110, N) :|: V110 >= 0, z = N, z' = 1 + (1 + V110), N >= 0 a__plus(z, z') -{ 2 }-> a__U41(a__U11(a__isNat(V19), V24), 1 + V19 + V24, N) :|: V24 >= 0, V19 >= 0, z = N, z' = 1 + (1 + V19 + V24), N >= 0 a__plus(z, z') -{ 2 }-> a__U41(1, 0, N) :|: z = N, z' = 1 + 0, N >= 0 a__plus(z, z') -{ 2 }-> a__U41(1 + M, M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0 a__plus(z, z') -{ 2 }-> a__U31(a__U21(a__isNat(V18)), 1 + V18) :|: V18 >= 0, z = 1 + V18, z' = 0 a__plus(z, z') -{ 2 }-> a__U31(a__U11(a__isNat(V17), V23), 1 + V17 + V23) :|: z = 1 + V17 + V23, V23 >= 0, V17 >= 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U31(1, 0) :|: z = 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U31(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__isNat(X) :|: z = 1 + X, X >= 0 mark(z) -{ 2 }-> a__U42(a__plus(mark(X188), mark(X288)), X2, X3) :|: z = 1 + (1 + X188 + X288) + X2 + X3, X288 >= 0, X3 >= 0, X188 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U42(a__isNat(X94), X2, X3) :|: z = 1 + (1 + X94) + X2 + X3, X3 >= 0, X2 >= 0, X94 >= 0 mark(z) -{ 2 }-> a__U42(a__U42(mark(X187), X287, X338), X2, X3) :|: X187 >= 0, X3 >= 0, z = 1 + (1 + X187 + X287 + X338) + X2 + X3, X338 >= 0, X287 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U42(a__U41(mark(X186), X286, X337), X2, X3) :|: X286 >= 0, z = 1 + (1 + X186 + X286 + X337) + X2 + X3, X186 >= 0, X3 >= 0, X2 >= 0, X337 >= 0 mark(z) -{ 2 }-> a__U42(a__U31(mark(X185), X285), X2, X3) :|: X285 >= 0, X185 >= 0, X3 >= 0, z = 1 + (1 + X185 + X285) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> a__U42(a__U21(mark(X95)), X2, X3) :|: X95 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X95) + X2 + X3 mark(z) -{ 2 }-> a__U42(a__U12(mark(X93)), X2, X3) :|: z = 1 + (1 + X93) + X2 + X3, X3 >= 0, X2 >= 0, X93 >= 0 mark(z) -{ 2 }-> a__U42(a__U11(mark(X184), X284), X2, X3) :|: z = 1 + (1 + X184 + X284) + X2 + X3, X184 >= 0, X284 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U42(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U42(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U42(1 + mark(X96), X2, X3) :|: X96 >= 0, z = 1 + (1 + X96) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__plus(mark(X183), mark(X283)), X2, X3) :|: X183 >= 0, X283 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X183 + X283) + X2 + X3 mark(z) -{ 2 }-> a__U41(a__isNat(X90), X2, X3) :|: z = 1 + (1 + X90) + X2 + X3, X90 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U42(mark(X182), X282, X336), X2, X3) :|: z = 1 + (1 + X182 + X282 + X336) + X2 + X3, X282 >= 0, X3 >= 0, X182 >= 0, X2 >= 0, X336 >= 0 mark(z) -{ 2 }-> a__U41(a__U41(mark(X181), X281, X335), X2, X3) :|: X181 >= 0, X3 >= 0, z = 1 + (1 + X181 + X281 + X335) + X2 + X3, X335 >= 0, X281 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U31(mark(X180), X280), X2, X3) :|: X280 >= 0, X3 >= 0, z = 1 + (1 + X180 + X280) + X2 + X3, X2 >= 0, X180 >= 0 mark(z) -{ 2 }-> a__U41(a__U21(mark(X91)), X2, X3) :|: z = 1 + (1 + X91) + X2 + X3, X91 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U12(mark(X89)), X2, X3) :|: X89 >= 0, X3 >= 0, z = 1 + (1 + X89) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U11(mark(X179), X279), X2, X3) :|: X279 >= 0, X3 >= 0, z = 1 + (1 + X179 + X279) + X2 + X3, X2 >= 0, X179 >= 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(X92), X2, X3) :|: X92 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X92) + X2 + X3 mark(z) -{ 2 }-> a__U31(a__plus(mark(X178), mark(X278)), X2) :|: z = 1 + (1 + X178 + X278) + X2, X2 >= 0, X178 >= 0, X278 >= 0 mark(z) -{ 2 }-> a__U31(a__isNat(X86), X2) :|: X86 >= 0, z = 1 + (1 + X86) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U42(mark(X177), X277, X334), X2) :|: X177 >= 0, z = 1 + (1 + X177 + X277 + X334) + X2, X334 >= 0, X2 >= 0, X277 >= 0 mark(z) -{ 2 }-> a__U31(a__U41(mark(X176), X276, X333), X2) :|: X176 >= 0, X276 >= 0, X333 >= 0, X2 >= 0, z = 1 + (1 + X176 + X276 + X333) + X2 mark(z) -{ 2 }-> a__U31(a__U31(mark(X175), X275), X2) :|: X275 >= 0, X175 >= 0, z = 1 + (1 + X175 + X275) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U21(mark(X87)), X2) :|: X87 >= 0, X2 >= 0, z = 1 + (1 + X87) + X2 mark(z) -{ 2 }-> a__U31(a__U12(mark(X85)), X2) :|: X85 >= 0, z = 1 + (1 + X85) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U11(mark(X174), X274), X2) :|: X174 >= 0, X274 >= 0, z = 1 + (1 + X174 + X274) + X2, X2 >= 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(X88), X2) :|: z = 1 + (1 + X88) + X2, X88 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__plus(mark(X173), mark(X273))) :|: z = 1 + (1 + X173 + X273), X173 >= 0, X273 >= 0 mark(z) -{ 2 }-> a__U21(a__isNat(X82)) :|: X82 >= 0, z = 1 + (1 + X82) mark(z) -{ 2 }-> a__U21(a__U42(mark(X172), X272, X332)) :|: X172 >= 0, X272 >= 0, z = 1 + (1 + X172 + X272 + X332), X332 >= 0 mark(z) -{ 2 }-> a__U21(a__U41(mark(X171), X271, X331)) :|: X271 >= 0, z = 1 + (1 + X171 + X271 + X331), X331 >= 0, X171 >= 0 mark(z) -{ 2 }-> a__U21(a__U31(mark(X170), X270)) :|: z = 1 + (1 + X170 + X270), X170 >= 0, X270 >= 0 mark(z) -{ 2 }-> a__U21(a__U21(mark(X83))) :|: z = 1 + (1 + X83), X83 >= 0 mark(z) -{ 2 }-> a__U21(a__U12(mark(X81))) :|: X81 >= 0, z = 1 + (1 + X81) mark(z) -{ 2 }-> a__U21(a__U11(mark(X169), X269)) :|: X269 >= 0, X169 >= 0, z = 1 + (1 + X169 + X269) mark(z) -{ 2 }-> a__U21(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__U21(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__U21(1 + mark(X84)) :|: z = 1 + (1 + X84), X84 >= 0 mark(z) -{ 2 }-> a__U12(a__plus(mark(X168), mark(X268))) :|: X168 >= 0, X268 >= 0, z = 1 + (1 + X168 + X268) mark(z) -{ 2 }-> a__U12(a__isNat(X78)) :|: z = 1 + (1 + X78), X78 >= 0 mark(z) -{ 2 }-> a__U12(a__U42(mark(X167), X267, X330)) :|: X267 >= 0, z = 1 + (1 + X167 + X267 + X330), X330 >= 0, X167 >= 0 mark(z) -{ 2 }-> a__U12(a__U41(mark(X166), X266, X329)) :|: X166 >= 0, X329 >= 0, X266 >= 0, z = 1 + (1 + X166 + X266 + X329) mark(z) -{ 2 }-> a__U12(a__U31(mark(X165), X265)) :|: X265 >= 0, X165 >= 0, z = 1 + (1 + X165 + X265) mark(z) -{ 2 }-> a__U12(a__U21(mark(X79))) :|: X79 >= 0, z = 1 + (1 + X79) mark(z) -{ 2 }-> a__U12(a__U12(mark(X77))) :|: X77 >= 0, z = 1 + (1 + X77) mark(z) -{ 2 }-> a__U12(a__U11(mark(X164), X264)) :|: X264 >= 0, z = 1 + (1 + X164 + X264), X164 >= 0 mark(z) -{ 2 }-> a__U12(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__U12(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__U12(1 + mark(X80)) :|: z = 1 + (1 + X80), X80 >= 0 mark(z) -{ 2 }-> a__U11(a__plus(mark(X163), mark(X263)), X2) :|: X163 >= 0, z = 1 + (1 + X163 + X263) + X2, X263 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__isNat(X74), X2) :|: z = 1 + (1 + X74) + X2, X2 >= 0, X74 >= 0 mark(z) -{ 2 }-> a__U11(a__U42(mark(X162), X262, X328), X2) :|: X162 >= 0, X262 >= 0, X328 >= 0, z = 1 + (1 + X162 + X262 + X328) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U41(mark(X161), X261, X327), X2) :|: X261 >= 0, z = 1 + (1 + X161 + X261 + X327) + X2, X327 >= 0, X2 >= 0, X161 >= 0 mark(z) -{ 2 }-> a__U11(a__U31(mark(X160), X260), X2) :|: X160 >= 0, z = 1 + (1 + X160 + X260) + X2, X260 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U21(mark(X75)), X2) :|: X75 >= 0, z = 1 + (1 + X75) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U12(mark(X73)), X2) :|: X73 >= 0, z = 1 + (1 + X73) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U11(mark(X159), X259), X2) :|: X259 >= 0, z = 1 + (1 + X159 + X259) + X2, X2 >= 0, X159 >= 0 mark(z) -{ 2 }-> a__U11(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(1 + mark(X76), X2) :|: X76 >= 0, X2 >= 0, z = 1 + (1 + X76) + X2 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__U12(z) -{ 1 }-> 1 :|: z = 1 a__U12(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U21(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U21(z) -{ 1 }-> 1 :|: z = 1 ---------------------------------------- (16) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z') -{ 2 }-> a__U12(a__U21(a__isNat(V1''))) :|: V1'' >= 0, z = 1, z' = 1 + V1'' a__U11(z, z') -{ 2 }-> a__U12(a__U11(a__isNat(V1'), V2')) :|: z = 1, z' = 1 + V1' + V2', V2' >= 0, V1' >= 0 a__U11(z, z') -{ 3 }-> 1 :|: z = 1, z' = 0, 1 = 1 a__U11(z, z') -{ 3 }-> 1 :|: z' = V2, z = 1, V2 >= 0, 1 + V2 = 1 a__U11(z, z') -{ 3 }-> 1 + X :|: z = 1, z' = 0, X >= 0, 1 = X a__U11(z, z') -{ 3 }-> 1 + X :|: z' = V2, z = 1, V2 >= 0, X >= 0, 1 + V2 = X a__U11(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U12(z) -{ 1 }-> 1 :|: z = 1 a__U12(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U21(z) -{ 1 }-> 1 :|: z = 1 a__U21(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U31(z, z') -{ 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'') -{ 2 }-> a__U42(a__U21(a__isNat(V12)), M, 1 + V12) :|: z' = M, z = 1, z'' = 1 + V12, V12 >= 0, M >= 0 a__U41(z, z', z'') -{ 2 }-> a__U42(a__U11(a__isNat(V11), V2''), M, 1 + V11 + V2'') :|: z' = M, V11 >= 0, V2'' >= 0, z = 1, z'' = 1 + V11 + V2'', M >= 0 a__U41(z, z', z'') -{ 2 }-> a__U42(1, M, 0) :|: z'' = 0, z' = M, z = 1, M >= 0 a__U41(z, z', z'') -{ 2 }-> a__U42(1 + N, M, N) :|: 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__U42(z, z', z'') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U42(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__isNat(z) -{ 2 }-> a__U21(a__U21(a__isNat(V16))) :|: z = 1 + (1 + V16), V16 >= 0 a__isNat(z) -{ 2 }-> a__U21(a__U11(a__isNat(V15), V22)) :|: z = 1 + (1 + V15 + V22), V22 >= 0, V15 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__U21(a__isNat(V14)), V2) :|: V14 >= 0, z = 1 + (1 + V14) + V2, V2 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__U11(a__isNat(V13), V21), V2) :|: V21 >= 0, V13 >= 0, V2 >= 0, z = 1 + (1 + V13 + V21) + V2 a__isNat(z) -{ 2 }-> a__U11(1, V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNat(z) -{ 2 }-> a__U11(1 + V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNat(z) -{ 1 }-> 1 :|: z = 0 a__isNat(z) -{ 3 }-> 1 :|: z = 1 + 0, 1 = 1 a__isNat(z) -{ 3 }-> 1 :|: z = 1 + V1, V1 >= 0, 1 + V1 = 1 a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__isNat(z) -{ 3 }-> 1 + X :|: z = 1 + 0, X >= 0, 1 = X a__isNat(z) -{ 3 }-> 1 + X :|: z = 1 + V1, V1 >= 0, X >= 0, 1 + V1 = X a__plus(z, z') -{ 2 }-> a__U41(a__U21(a__isNat(V110)), 1 + V110, N) :|: V110 >= 0, z = N, z' = 1 + (1 + V110), N >= 0 a__plus(z, z') -{ 2 }-> a__U41(a__U11(a__isNat(V19), V24), 1 + V19 + V24, N) :|: V24 >= 0, V19 >= 0, z = N, z' = 1 + (1 + V19 + V24), N >= 0 a__plus(z, z') -{ 2 }-> a__U41(1, 0, N) :|: z = N, z' = 1 + 0, N >= 0 a__plus(z, z') -{ 2 }-> a__U41(1 + M, M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0 a__plus(z, z') -{ 2 }-> a__U31(a__U21(a__isNat(V18)), 1 + V18) :|: V18 >= 0, z = 1 + V18, z' = 0 a__plus(z, z') -{ 2 }-> a__U31(a__U11(a__isNat(V17), V23), 1 + V17 + V23) :|: z = 1 + V17 + V23, V23 >= 0, V17 >= 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U31(1, 0) :|: z = 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U31(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__isNat(X) :|: z = 1 + X, X >= 0 mark(z) -{ 2 }-> a__U42(a__plus(mark(X188), mark(X288)), X2, X3) :|: z = 1 + (1 + X188 + X288) + X2 + X3, X288 >= 0, X3 >= 0, X188 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U42(a__isNat(X94), X2, X3) :|: z = 1 + (1 + X94) + X2 + X3, X3 >= 0, X2 >= 0, X94 >= 0 mark(z) -{ 2 }-> a__U42(a__U42(mark(X187), X287, X338), X2, X3) :|: X187 >= 0, X3 >= 0, z = 1 + (1 + X187 + X287 + X338) + X2 + X3, X338 >= 0, X287 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U42(a__U41(mark(X186), X286, X337), X2, X3) :|: X286 >= 0, z = 1 + (1 + X186 + X286 + X337) + X2 + X3, X186 >= 0, X3 >= 0, X2 >= 0, X337 >= 0 mark(z) -{ 2 }-> a__U42(a__U31(mark(X185), X285), X2, X3) :|: X285 >= 0, X185 >= 0, X3 >= 0, z = 1 + (1 + X185 + X285) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> a__U42(a__U21(mark(X95)), X2, X3) :|: X95 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X95) + X2 + X3 mark(z) -{ 2 }-> a__U42(a__U12(mark(X93)), X2, X3) :|: z = 1 + (1 + X93) + X2 + X3, X3 >= 0, X2 >= 0, X93 >= 0 mark(z) -{ 2 }-> a__U42(a__U11(mark(X184), X284), X2, X3) :|: z = 1 + (1 + X184 + X284) + X2 + X3, X184 >= 0, X284 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U42(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U42(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U42(1 + mark(X96), X2, X3) :|: X96 >= 0, z = 1 + (1 + X96) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__plus(mark(X183), mark(X283)), X2, X3) :|: X183 >= 0, X283 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X183 + X283) + X2 + X3 mark(z) -{ 2 }-> a__U41(a__isNat(X90), X2, X3) :|: z = 1 + (1 + X90) + X2 + X3, X90 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U42(mark(X182), X282, X336), X2, X3) :|: z = 1 + (1 + X182 + X282 + X336) + X2 + X3, X282 >= 0, X3 >= 0, X182 >= 0, X2 >= 0, X336 >= 0 mark(z) -{ 2 }-> a__U41(a__U41(mark(X181), X281, X335), X2, X3) :|: X181 >= 0, X3 >= 0, z = 1 + (1 + X181 + X281 + X335) + X2 + X3, X335 >= 0, X281 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U31(mark(X180), X280), X2, X3) :|: X280 >= 0, X3 >= 0, z = 1 + (1 + X180 + X280) + X2 + X3, X2 >= 0, X180 >= 0 mark(z) -{ 2 }-> a__U41(a__U21(mark(X91)), X2, X3) :|: z = 1 + (1 + X91) + X2 + X3, X91 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U12(mark(X89)), X2, X3) :|: X89 >= 0, X3 >= 0, z = 1 + (1 + X89) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U11(mark(X179), X279), X2, X3) :|: X279 >= 0, X3 >= 0, z = 1 + (1 + X179 + X279) + X2 + X3, X2 >= 0, X179 >= 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(X92), X2, X3) :|: X92 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X92) + X2 + X3 mark(z) -{ 2 }-> a__U31(a__plus(mark(X178), mark(X278)), X2) :|: z = 1 + (1 + X178 + X278) + X2, X2 >= 0, X178 >= 0, X278 >= 0 mark(z) -{ 2 }-> a__U31(a__isNat(X86), X2) :|: X86 >= 0, z = 1 + (1 + X86) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U42(mark(X177), X277, X334), X2) :|: X177 >= 0, z = 1 + (1 + X177 + X277 + X334) + X2, X334 >= 0, X2 >= 0, X277 >= 0 mark(z) -{ 2 }-> a__U31(a__U41(mark(X176), X276, X333), X2) :|: X176 >= 0, X276 >= 0, X333 >= 0, X2 >= 0, z = 1 + (1 + X176 + X276 + X333) + X2 mark(z) -{ 2 }-> a__U31(a__U31(mark(X175), X275), X2) :|: X275 >= 0, X175 >= 0, z = 1 + (1 + X175 + X275) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U21(mark(X87)), X2) :|: X87 >= 0, X2 >= 0, z = 1 + (1 + X87) + X2 mark(z) -{ 2 }-> a__U31(a__U12(mark(X85)), X2) :|: X85 >= 0, z = 1 + (1 + X85) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U11(mark(X174), X274), X2) :|: X174 >= 0, X274 >= 0, z = 1 + (1 + X174 + X274) + X2, X2 >= 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(X88), X2) :|: z = 1 + (1 + X88) + X2, X88 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__plus(mark(X173), mark(X273))) :|: z = 1 + (1 + X173 + X273), X173 >= 0, X273 >= 0 mark(z) -{ 2 }-> a__U21(a__isNat(X82)) :|: X82 >= 0, z = 1 + (1 + X82) mark(z) -{ 2 }-> a__U21(a__U42(mark(X172), X272, X332)) :|: X172 >= 0, X272 >= 0, z = 1 + (1 + X172 + X272 + X332), X332 >= 0 mark(z) -{ 2 }-> a__U21(a__U41(mark(X171), X271, X331)) :|: X271 >= 0, z = 1 + (1 + X171 + X271 + X331), X331 >= 0, X171 >= 0 mark(z) -{ 2 }-> a__U21(a__U31(mark(X170), X270)) :|: z = 1 + (1 + X170 + X270), X170 >= 0, X270 >= 0 mark(z) -{ 2 }-> a__U21(a__U21(mark(X83))) :|: z = 1 + (1 + X83), X83 >= 0 mark(z) -{ 2 }-> a__U21(a__U12(mark(X81))) :|: X81 >= 0, z = 1 + (1 + X81) mark(z) -{ 2 }-> a__U21(a__U11(mark(X169), X269)) :|: X269 >= 0, X169 >= 0, z = 1 + (1 + X169 + X269) mark(z) -{ 2 }-> a__U21(1 + mark(X84)) :|: z = 1 + (1 + X84), X84 >= 0 mark(z) -{ 2 }-> a__U12(a__plus(mark(X168), mark(X268))) :|: X168 >= 0, X268 >= 0, z = 1 + (1 + X168 + X268) mark(z) -{ 2 }-> a__U12(a__isNat(X78)) :|: z = 1 + (1 + X78), X78 >= 0 mark(z) -{ 2 }-> a__U12(a__U42(mark(X167), X267, X330)) :|: X267 >= 0, z = 1 + (1 + X167 + X267 + X330), X330 >= 0, X167 >= 0 mark(z) -{ 2 }-> a__U12(a__U41(mark(X166), X266, X329)) :|: X166 >= 0, X329 >= 0, X266 >= 0, z = 1 + (1 + X166 + X266 + X329) mark(z) -{ 2 }-> a__U12(a__U31(mark(X165), X265)) :|: X265 >= 0, X165 >= 0, z = 1 + (1 + X165 + X265) mark(z) -{ 2 }-> a__U12(a__U21(mark(X79))) :|: X79 >= 0, z = 1 + (1 + X79) mark(z) -{ 2 }-> a__U12(a__U12(mark(X77))) :|: X77 >= 0, z = 1 + (1 + X77) mark(z) -{ 2 }-> a__U12(a__U11(mark(X164), X264)) :|: X264 >= 0, z = 1 + (1 + X164 + X264), X164 >= 0 mark(z) -{ 2 }-> a__U12(1 + mark(X80)) :|: z = 1 + (1 + X80), X80 >= 0 mark(z) -{ 2 }-> a__U11(a__plus(mark(X163), mark(X263)), X2) :|: X163 >= 0, z = 1 + (1 + X163 + X263) + X2, X263 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__isNat(X74), X2) :|: z = 1 + (1 + X74) + X2, X2 >= 0, X74 >= 0 mark(z) -{ 2 }-> a__U11(a__U42(mark(X162), X262, X328), X2) :|: X162 >= 0, X262 >= 0, X328 >= 0, z = 1 + (1 + X162 + X262 + X328) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U41(mark(X161), X261, X327), X2) :|: X261 >= 0, z = 1 + (1 + X161 + X261 + X327) + X2, X327 >= 0, X2 >= 0, X161 >= 0 mark(z) -{ 2 }-> a__U11(a__U31(mark(X160), X260), X2) :|: X160 >= 0, z = 1 + (1 + X160 + X260) + X2, X260 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U21(mark(X75)), X2) :|: X75 >= 0, z = 1 + (1 + X75) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U12(mark(X73)), X2) :|: X73 >= 0, z = 1 + (1 + X73) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U11(mark(X159), X259), X2) :|: X259 >= 0, z = 1 + (1 + X159 + X259) + X2, X2 >= 0, X159 >= 0 mark(z) -{ 2 }-> a__U11(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(1 + mark(X76), X2) :|: X76 >= 0, X2 >= 0, z = 1 + (1 + X76) + X2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 3 }-> 1 :|: z = 1 + 1, 1 = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 3 }-> 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') -{ 2 }-> a__U12(a__U21(a__isNat(z' - 1))) :|: z' - 1 >= 0, z = 1 a__U11(z, z') -{ 2 }-> a__U12(a__U11(a__isNat(V1'), V2')) :|: z = 1, z' = 1 + V1' + V2', V2' >= 0, V1' >= 0 a__U11(z, z') -{ 3 }-> 1 :|: z = 1, z' = 0, 1 = 1 a__U11(z, z') -{ 3 }-> 1 :|: z = 1, z' >= 0, 1 + z' = 1 a__U11(z, z') -{ 3 }-> 1 + X :|: z = 1, z' = 0, X >= 0, 1 = X a__U11(z, z') -{ 3 }-> 1 + X :|: z = 1, z' >= 0, X >= 0, 1 + z' = X a__U11(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U12(z) -{ 1 }-> 1 :|: z = 1 a__U12(z) -{ 1 }-> 1 + z :|: z >= 0 a__U21(z) -{ 1 }-> 1 :|: z = 1 a__U21(z) -{ 1 }-> 1 + z :|: z >= 0 a__U31(z, z') -{ 1 }-> mark(z') :|: z = 1, z' >= 0 a__U31(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U41(z, z', z'') -{ 2 }-> a__U42(a__U21(a__isNat(z'' - 1)), z', 1 + (z'' - 1)) :|: z = 1, z'' - 1 >= 0, z' >= 0 a__U41(z, z', z'') -{ 2 }-> a__U42(a__U11(a__isNat(V11), V2''), z', 1 + V11 + V2'') :|: V11 >= 0, V2'' >= 0, z = 1, z'' = 1 + V11 + V2'', z' >= 0 a__U41(z, z', z'') -{ 2 }-> a__U42(1, z', 0) :|: z'' = 0, z = 1, z' >= 0 a__U41(z, z', z'') -{ 2 }-> a__U42(1 + z'', z', z'') :|: z = 1, z' >= 0, z'' >= 0 a__U41(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0 a__U42(z, z', z'') -{ 1 }-> 1 + a__plus(mark(z''), mark(z')) :|: z = 1, z' >= 0, z'' >= 0 a__U42(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0 a__isNat(z) -{ 2 }-> a__U21(a__U21(a__isNat(z - 2))) :|: z - 2 >= 0 a__isNat(z) -{ 2 }-> a__U21(a__U11(a__isNat(V15), V22)) :|: z = 1 + (1 + V15 + V22), V22 >= 0, V15 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__U21(a__isNat(V14)), V2) :|: V14 >= 0, z = 1 + (1 + V14) + V2, V2 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__U11(a__isNat(V13), V21), V2) :|: V21 >= 0, V13 >= 0, V2 >= 0, z = 1 + (1 + V13 + V21) + V2 a__isNat(z) -{ 2 }-> a__U11(1, z - 1) :|: z - 1 >= 0 a__isNat(z) -{ 2 }-> a__U11(1 + V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNat(z) -{ 1 }-> 1 :|: z = 0 a__isNat(z) -{ 3 }-> 1 :|: z = 1 + 0, 1 = 1 a__isNat(z) -{ 3 }-> 1 :|: z - 1 >= 0, 1 + (z - 1) = 1 a__isNat(z) -{ 3 }-> 1 + X :|: z = 1 + 0, X >= 0, 1 = X a__isNat(z) -{ 3 }-> 1 + X :|: z - 1 >= 0, X >= 0, 1 + (z - 1) = X a__isNat(z) -{ 1 }-> 1 + z :|: z >= 0 a__plus(z, z') -{ 2 }-> a__U41(a__U21(a__isNat(z' - 2)), 1 + (z' - 2), z) :|: z' - 2 >= 0, z >= 0 a__plus(z, z') -{ 2 }-> a__U41(a__U11(a__isNat(V19), V24), 1 + V19 + V24, z) :|: V24 >= 0, V19 >= 0, z' = 1 + (1 + V19 + V24), z >= 0 a__plus(z, z') -{ 2 }-> a__U41(1, 0, z) :|: z' = 1 + 0, z >= 0 a__plus(z, z') -{ 2 }-> a__U41(1 + (z' - 1), z' - 1, z) :|: z' - 1 >= 0, z >= 0 a__plus(z, z') -{ 2 }-> a__U31(a__U21(a__isNat(z - 1)), 1 + (z - 1)) :|: z - 1 >= 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U31(a__U11(a__isNat(V17), V23), 1 + V17 + V23) :|: z = 1 + V17 + V23, V23 >= 0, V17 >= 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U31(1, 0) :|: z = 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U31(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__isNat(z - 1) :|: z - 1 >= 0 mark(z) -{ 2 }-> a__U42(a__plus(mark(X188), mark(X288)), X2, X3) :|: z = 1 + (1 + X188 + X288) + X2 + X3, X288 >= 0, X3 >= 0, X188 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U42(a__isNat(X94), X2, X3) :|: z = 1 + (1 + X94) + X2 + X3, X3 >= 0, X2 >= 0, X94 >= 0 mark(z) -{ 2 }-> a__U42(a__U42(mark(X187), X287, X338), X2, X3) :|: X187 >= 0, X3 >= 0, z = 1 + (1 + X187 + X287 + X338) + X2 + X3, X338 >= 0, X287 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U42(a__U41(mark(X186), X286, X337), X2, X3) :|: X286 >= 0, z = 1 + (1 + X186 + X286 + X337) + X2 + X3, X186 >= 0, X3 >= 0, X2 >= 0, X337 >= 0 mark(z) -{ 2 }-> a__U42(a__U31(mark(X185), X285), X2, X3) :|: X285 >= 0, X185 >= 0, X3 >= 0, z = 1 + (1 + X185 + X285) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> a__U42(a__U21(mark(X95)), X2, X3) :|: X95 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X95) + X2 + X3 mark(z) -{ 2 }-> a__U42(a__U12(mark(X93)), X2, X3) :|: z = 1 + (1 + X93) + X2 + X3, X3 >= 0, X2 >= 0, X93 >= 0 mark(z) -{ 2 }-> a__U42(a__U11(mark(X184), X284), X2, X3) :|: z = 1 + (1 + X184 + X284) + X2 + X3, X184 >= 0, X284 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U42(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U42(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U42(1 + mark(X96), X2, X3) :|: X96 >= 0, z = 1 + (1 + X96) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__plus(mark(X183), mark(X283)), X2, X3) :|: X183 >= 0, X283 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X183 + X283) + X2 + X3 mark(z) -{ 2 }-> a__U41(a__isNat(X90), X2, X3) :|: z = 1 + (1 + X90) + X2 + X3, X90 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U42(mark(X182), X282, X336), X2, X3) :|: z = 1 + (1 + X182 + X282 + X336) + X2 + X3, X282 >= 0, X3 >= 0, X182 >= 0, X2 >= 0, X336 >= 0 mark(z) -{ 2 }-> a__U41(a__U41(mark(X181), X281, X335), X2, X3) :|: X181 >= 0, X3 >= 0, z = 1 + (1 + X181 + X281 + X335) + X2 + X3, X335 >= 0, X281 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U31(mark(X180), X280), X2, X3) :|: X280 >= 0, X3 >= 0, z = 1 + (1 + X180 + X280) + X2 + X3, X2 >= 0, X180 >= 0 mark(z) -{ 2 }-> a__U41(a__U21(mark(X91)), X2, X3) :|: z = 1 + (1 + X91) + X2 + X3, X91 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U12(mark(X89)), X2, X3) :|: X89 >= 0, X3 >= 0, z = 1 + (1 + X89) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U11(mark(X179), X279), X2, X3) :|: X279 >= 0, X3 >= 0, z = 1 + (1 + X179 + X279) + X2 + X3, X2 >= 0, X179 >= 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(X92), X2, X3) :|: X92 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X92) + X2 + X3 mark(z) -{ 2 }-> a__U31(a__plus(mark(X178), mark(X278)), X2) :|: z = 1 + (1 + X178 + X278) + X2, X2 >= 0, X178 >= 0, X278 >= 0 mark(z) -{ 2 }-> a__U31(a__isNat(X86), X2) :|: X86 >= 0, z = 1 + (1 + X86) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U42(mark(X177), X277, X334), X2) :|: X177 >= 0, z = 1 + (1 + X177 + X277 + X334) + X2, X334 >= 0, X2 >= 0, X277 >= 0 mark(z) -{ 2 }-> a__U31(a__U41(mark(X176), X276, X333), X2) :|: X176 >= 0, X276 >= 0, X333 >= 0, X2 >= 0, z = 1 + (1 + X176 + X276 + X333) + X2 mark(z) -{ 2 }-> a__U31(a__U31(mark(X175), X275), X2) :|: X275 >= 0, X175 >= 0, z = 1 + (1 + X175 + X275) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U21(mark(X87)), X2) :|: X87 >= 0, X2 >= 0, z = 1 + (1 + X87) + X2 mark(z) -{ 2 }-> a__U31(a__U12(mark(X85)), X2) :|: X85 >= 0, z = 1 + (1 + X85) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U11(mark(X174), X274), X2) :|: X174 >= 0, X274 >= 0, z = 1 + (1 + X174 + X274) + X2, X2 >= 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(X88), X2) :|: z = 1 + (1 + X88) + X2, X88 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__plus(mark(X173), mark(X273))) :|: z = 1 + (1 + X173 + X273), X173 >= 0, X273 >= 0 mark(z) -{ 2 }-> a__U21(a__isNat(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U21(a__U42(mark(X172), X272, X332)) :|: X172 >= 0, X272 >= 0, z = 1 + (1 + X172 + X272 + X332), X332 >= 0 mark(z) -{ 2 }-> a__U21(a__U41(mark(X171), X271, X331)) :|: X271 >= 0, z = 1 + (1 + X171 + X271 + X331), X331 >= 0, X171 >= 0 mark(z) -{ 2 }-> a__U21(a__U31(mark(X170), X270)) :|: z = 1 + (1 + X170 + X270), X170 >= 0, X270 >= 0 mark(z) -{ 2 }-> a__U21(a__U21(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U21(a__U12(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U21(a__U11(mark(X169), X269)) :|: X269 >= 0, X169 >= 0, z = 1 + (1 + X169 + X269) mark(z) -{ 2 }-> a__U21(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U12(a__plus(mark(X168), mark(X268))) :|: X168 >= 0, X268 >= 0, z = 1 + (1 + X168 + X268) mark(z) -{ 2 }-> a__U12(a__isNat(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U12(a__U42(mark(X167), X267, X330)) :|: X267 >= 0, z = 1 + (1 + X167 + X267 + X330), X330 >= 0, X167 >= 0 mark(z) -{ 2 }-> a__U12(a__U41(mark(X166), X266, X329)) :|: X166 >= 0, X329 >= 0, X266 >= 0, z = 1 + (1 + X166 + X266 + X329) mark(z) -{ 2 }-> a__U12(a__U31(mark(X165), X265)) :|: X265 >= 0, X165 >= 0, z = 1 + (1 + X165 + X265) mark(z) -{ 2 }-> a__U12(a__U21(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U12(a__U12(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U12(a__U11(mark(X164), X264)) :|: X264 >= 0, z = 1 + (1 + X164 + X264), X164 >= 0 mark(z) -{ 2 }-> a__U12(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U11(a__plus(mark(X163), mark(X263)), X2) :|: X163 >= 0, z = 1 + (1 + X163 + X263) + X2, X263 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__isNat(X74), X2) :|: z = 1 + (1 + X74) + X2, X2 >= 0, X74 >= 0 mark(z) -{ 2 }-> a__U11(a__U42(mark(X162), X262, X328), X2) :|: X162 >= 0, X262 >= 0, X328 >= 0, z = 1 + (1 + X162 + X262 + X328) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U41(mark(X161), X261, X327), X2) :|: X261 >= 0, z = 1 + (1 + X161 + X261 + X327) + X2, X327 >= 0, X2 >= 0, X161 >= 0 mark(z) -{ 2 }-> a__U11(a__U31(mark(X160), X260), X2) :|: X160 >= 0, z = 1 + (1 + X160 + X260) + X2, X260 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U21(mark(X75)), X2) :|: X75 >= 0, z = 1 + (1 + X75) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U12(mark(X73)), X2) :|: X73 >= 0, z = 1 + (1 + X73) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U11(mark(X159), X259), X2) :|: X259 >= 0, z = 1 + (1 + X159 + X259) + X2, X2 >= 0, X159 >= 0 mark(z) -{ 2 }-> a__U11(1, z - 2) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U11(0, z - 1) :|: z - 1 >= 0 mark(z) -{ 2 }-> a__U11(1 + mark(X76), X2) :|: X76 >= 0, X2 >= 0, z = 1 + (1 + X76) + X2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 3 }-> 1 :|: z = 1 + 1, 1 = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 3 }-> 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, V2) -> a__U12(a__isNat(V2)) [1] a__U12(tt) -> tt [1] a__U21(tt) -> tt [1] a__U31(tt, N) -> mark(N) [1] a__U41(tt, M, N) -> a__U42(a__isNat(N), M, N) [1] a__U42(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1] a__isNat(0) -> tt [1] a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2) [1] a__isNat(s(V1)) -> a__U21(a__isNat(V1)) [1] a__plus(N, 0) -> a__U31(a__isNat(N), N) [1] a__plus(N, s(M)) -> a__U41(a__isNat(M), M, N) [1] mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1] mark(U12(X)) -> a__U12(mark(X)) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(U21(X)) -> a__U21(mark(X)) [1] mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1] mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1] mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] a__U11(X1, X2) -> U11(X1, X2) [1] a__U12(X) -> U12(X) [1] a__isNat(X) -> isNat(X) [1] a__U21(X) -> U21(X) [1] a__U31(X1, X2) -> U31(X1, X2) [1] a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1] a__U42(X1, X2, X3) -> U42(X1, X2, X3) [1] a__plus(X1, X2) -> plus(X1, X2) [1] The TRS has the following type information: a__U11 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 tt :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 a__U12 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 a__isNat :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 a__U21 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 a__U31 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 mark :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 a__U41 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 a__U42 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 s :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 a__plus :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 0 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 plus :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 U11 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 U12 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 isNat :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 U21 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 U31 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 U41 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 U42 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 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') -{ 1 }-> a__U12(a__isNat(V2)) :|: z' = V2, z = 1, V2 >= 0 a__U11(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U12(z) -{ 1 }-> 1 :|: z = 1 a__U12(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U21(z) -{ 1 }-> 1 :|: z = 1 a__U21(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U31(z, z') -{ 1 }-> 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 }-> a__U42(a__isNat(N), M, N) :|: 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__U42(z, z', z'') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U42(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__isNat(z) -{ 1 }-> a__U21(a__isNat(V1)) :|: z = 1 + V1, V1 >= 0 a__isNat(z) -{ 1 }-> a__U11(a__isNat(V1), V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNat(z) -{ 1 }-> 1 :|: z = 0 a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__plus(z, z') -{ 1 }-> a__U41(a__isNat(M), M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0 a__plus(z, z') -{ 1 }-> a__U31(a__isNat(N), N) :|: z = N, z' = 0, N >= 0 a__plus(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U42(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 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__U21(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U12(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U11(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (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) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(A__U12(a__isNat(z0)), A__ISNAT(z0)) A__U11(z0, z1) -> c1 A__U12(tt) -> c2 A__U12(z0) -> c3 A__U21(tt) -> c4 A__U21(z0) -> c5 A__U31(tt, z0) -> c6(MARK(z0)) A__U31(z0, z1) -> c7 A__U41(tt, z0, z1) -> c8(A__U42(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U41(z0, z1, z2) -> c9 A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U42(z0, z1, z2) -> c12 A__ISNAT(0) -> c13 A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__U21(a__isNat(z0)), A__ISNAT(z0)) A__ISNAT(z0) -> c16 A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__PLUS(z0, z1) -> c19 MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c21(A__U12(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U21(z0)) -> c23(A__U21(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c29 MARK(s(z0)) -> c30(MARK(z0)) MARK(0) -> c31 S tuples: A__U11(tt, z0) -> c(A__U12(a__isNat(z0)), A__ISNAT(z0)) A__U11(z0, z1) -> c1 A__U12(tt) -> c2 A__U12(z0) -> c3 A__U21(tt) -> c4 A__U21(z0) -> c5 A__U31(tt, z0) -> c6(MARK(z0)) A__U31(z0, z1) -> c7 A__U41(tt, z0, z1) -> c8(A__U42(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U41(z0, z1, z2) -> c9 A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U42(z0, z1, z2) -> c12 A__ISNAT(0) -> c13 A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__U21(a__isNat(z0)), A__ISNAT(z0)) A__ISNAT(z0) -> c16 A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__PLUS(z0, z1) -> c19 MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c21(A__U12(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U21(z0)) -> c23(A__U21(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c29 MARK(s(z0)) -> c30(MARK(z0)) MARK(0) -> c31 K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__U12_1, A__U21_1, A__U31_2, A__U41_3, A__U42_3, A__ISNAT_1, A__PLUS_2, MARK_1 Compound Symbols: c_2, c1, c2, c3, c4, c5, c6_1, c7, c8_2, c9, c10_2, c11_2, c12, c13, c14_2, c15_2, c16, c17_2, c18_2, c19, c20_2, c21_2, c22_1, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c29, c30_1, c31 ---------------------------------------- (25) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 13 trailing nodes: MARK(tt) -> c29 A__U31(z0, z1) -> c7 A__U21(tt) -> c4 A__U41(z0, z1, z2) -> c9 A__U21(z0) -> c5 A__U12(z0) -> c3 MARK(0) -> c31 A__ISNAT(0) -> c13 A__U11(z0, z1) -> c1 A__U12(tt) -> c2 A__ISNAT(z0) -> c16 A__U42(z0, z1, z2) -> c12 A__PLUS(z0, z1) -> c19 ---------------------------------------- (26) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(A__U12(a__isNat(z0)), A__ISNAT(z0)) A__U31(tt, z0) -> c6(MARK(z0)) A__U41(tt, z0, z1) -> c8(A__U42(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__U21(a__isNat(z0)), A__ISNAT(z0)) A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c21(A__U12(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U21(z0)) -> c23(A__U21(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) S tuples: A__U11(tt, z0) -> c(A__U12(a__isNat(z0)), A__ISNAT(z0)) A__U31(tt, z0) -> c6(MARK(z0)) A__U41(tt, z0, z1) -> c8(A__U42(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__U21(a__isNat(z0)), A__ISNAT(z0)) A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c21(A__U12(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U21(z0)) -> c23(A__U21(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__U31_2, A__U41_3, A__U42_3, A__ISNAT_1, A__PLUS_2, MARK_1 Compound Symbols: c_2, c6_1, c8_2, c10_2, c11_2, c14_2, c15_2, c17_2, c18_2, c20_2, c21_2, c22_1, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1 ---------------------------------------- (27) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (28) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) A__U41(tt, z0, z1) -> c8(A__U42(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) A__U41(tt, z0, z1) -> c8(A__U42(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__U41_3, A__U42_3, A__ISNAT_1, A__PLUS_2, MARK_1, A__U11_2 Compound Symbols: c6_1, c8_2, c10_2, c11_2, c14_2, c17_2, c18_2, c20_2, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1 ---------------------------------------- (29) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, z0, z1) -> c8(A__U42(a__isNat(z1), z0, z1), A__ISNAT(z1)) by A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0), A__ISNAT(0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, z0) -> c8(A__U42(isNat(z0), x0, z0), A__ISNAT(z0)) ---------------------------------------- (30) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0), A__ISNAT(0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, z0) -> c8(A__U42(isNat(z0), x0, z0), A__ISNAT(z0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0), A__ISNAT(0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, z0) -> c8(A__U42(isNat(z0), x0, z0), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__U42_3, A__ISNAT_1, A__PLUS_2, MARK_1, A__U11_2, A__U41_3 Compound Symbols: c6_1, c10_2, c11_2, c14_2, c17_2, c18_2, c20_2, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2 ---------------------------------------- (31) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (32) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__U42_3, A__ISNAT_1, A__PLUS_2, MARK_1, A__U11_2, A__U41_3 Compound Symbols: c6_1, c10_2, c11_2, c14_2, c17_2, c18_2, c20_2, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1 ---------------------------------------- (33) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1)) by A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, tt, x1) -> c10(A__PLUS(mark(x1), tt), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)), MARK(tt)) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)), MARK(0)) ---------------------------------------- (34) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, tt, x1) -> c10(A__PLUS(mark(x1), tt), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)), MARK(tt)) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)), MARK(0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, tt, x1) -> c10(A__PLUS(mark(x1), tt), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)), MARK(tt)) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__U42_3, A__ISNAT_1, A__PLUS_2, MARK_1, A__U11_2, A__U41_3 Compound Symbols: c6_1, c11_2, c14_2, c17_2, c18_2, c20_2, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2 ---------------------------------------- (35) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (36) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__U42_3, A__ISNAT_1, A__PLUS_2, MARK_1, A__U11_2, A__U41_3 Compound Symbols: c6_1, c11_2, c14_2, c17_2, c18_2, c20_2, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1 ---------------------------------------- (37) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0)) by A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, tt, x1) -> c11(A__PLUS(mark(x1), tt), MARK(tt)) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0), MARK(0)) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, tt, x1) -> c11(A__PLUS(mark(x1), tt), MARK(tt)) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0), MARK(0)) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, tt, x1) -> c11(A__PLUS(mark(x1), tt), MARK(tt)) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0), MARK(0)) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__ISNAT_1, A__PLUS_2, MARK_1, A__U11_2, A__U41_3, A__U42_3 Compound Symbols: c6_1, c14_2, c17_2, c18_2, c20_2, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2 ---------------------------------------- (39) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U42(tt, tt, x1) -> c11(A__PLUS(mark(x1), tt), MARK(tt)) ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0), MARK(0)) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0), MARK(0)) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__ISNAT_1, A__PLUS_2, MARK_1, A__U11_2, A__U41_3, A__U42_3 Compound Symbols: c6_1, c14_2, c17_2, c18_2, c20_2, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2 ---------------------------------------- (41) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (42) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__ISNAT_1, A__PLUS_2, MARK_1, A__U11_2, A__U41_3, A__U42_3 Compound Symbols: c6_1, c14_2, c17_2, c18_2, c20_2, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (43) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) by A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1), A__ISNAT(0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(z0, x1)) -> c14(A__U11(isNat(z0), x1), A__ISNAT(z0)) ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1), A__ISNAT(0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(z0, x1)) -> c14(A__U11(isNat(z0), x1), A__ISNAT(z0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1), A__ISNAT(0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(z0, x1)) -> c14(A__U11(isNat(z0), x1), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__PLUS_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3 Compound Symbols: c6_1, c17_2, c18_2, c20_2, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2 ---------------------------------------- (45) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__PLUS_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3 Compound Symbols: c6_1, c17_2, c18_2, c20_2, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1 ---------------------------------------- (47) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0)) by A__PLUS(0, 0) -> c17(A__U31(tt, 0), A__ISNAT(0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c17(A__U31(isNat(z0), z0), A__ISNAT(z0)) ---------------------------------------- (48) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(0, 0) -> c17(A__U31(tt, 0), A__ISNAT(0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c17(A__U31(isNat(z0), z0), A__ISNAT(z0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(0, 0) -> c17(A__U31(tt, 0), A__ISNAT(0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c17(A__U31(isNat(z0), z0), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__PLUS_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3 Compound Symbols: c6_1, c18_2, c20_2, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2 ---------------------------------------- (49) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, A__PLUS_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3 Compound Symbols: c6_1, c18_2, c20_2, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1 ---------------------------------------- (51) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) by A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0), A__ISNAT(0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c18(A__U41(isNat(z0), z0, x0), A__ISNAT(z0)) ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0), A__ISNAT(0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c18(A__U41(isNat(z0), z0, x0), A__ISNAT(z0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0), A__ISNAT(0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c18(A__U41(isNat(z0), z0, x0), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c20_2, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2 ---------------------------------------- (53) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c20_2, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (55) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) by MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c20(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c20(A__U11(s(mark(z0)), x1), MARK(s(z0))) MARK(U11(0, x1)) -> c20(A__U11(0, x1), MARK(0)) ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c20(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c20(A__U11(s(mark(z0)), x1), MARK(s(z0))) MARK(U11(0, x1)) -> c20(A__U11(0, x1), MARK(0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c20(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c20(A__U11(s(mark(z0)), x1), MARK(s(z0))) MARK(U11(0, x1)) -> c20(A__U11(0, x1), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2 ---------------------------------------- (57) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U11(0, x1)) -> c20(A__U11(0, x1), MARK(0)) ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c20(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c20(A__U11(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c20(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c20(A__U11(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2 ---------------------------------------- (59) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c20(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c20(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1 ---------------------------------------- (61) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1 ---------------------------------------- (63) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) by MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c24(A__U31(s(mark(z0)), x1), MARK(s(z0))) MARK(U31(0, x1)) -> c24(A__U31(0, x1), MARK(0)) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c24(A__U31(s(mark(z0)), x1), MARK(s(z0))) MARK(U31(0, x1)) -> c24(A__U31(0, x1), MARK(0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c24(A__U31(s(mark(z0)), x1), MARK(s(z0))) MARK(U31(0, x1)) -> c24(A__U31(0, x1), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2 ---------------------------------------- (65) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U31(0, x1)) -> c24(A__U31(0, x1), MARK(0)) ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c24(A__U31(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c24(A__U31(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2 ---------------------------------------- (67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1 ---------------------------------------- (69) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) by MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2), MARK(tt)) MARK(U41(s(z0), x1, x2)) -> c25(A__U41(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U41(0, x1, x2)) -> c25(A__U41(0, x1, x2), MARK(0)) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2), MARK(tt)) MARK(U41(s(z0), x1, x2)) -> c25(A__U41(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U41(0, x1, x2)) -> c25(A__U41(0, x1, x2), MARK(0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2), MARK(tt)) MARK(U41(s(z0), x1, x2)) -> c25(A__U41(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U41(0, x1, x2)) -> c25(A__U41(0, x1, x2), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2 ---------------------------------------- (71) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U41(0, x1, x2)) -> c25(A__U41(0, x1, x2), MARK(0)) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2), MARK(tt)) MARK(U41(s(z0), x1, x2)) -> c25(A__U41(s(mark(z0)), x1, x2), MARK(s(z0))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2), MARK(tt)) MARK(U41(s(z0), x1, x2)) -> c25(A__U41(s(mark(z0)), x1, x2), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2 ---------------------------------------- (73) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1 ---------------------------------------- (75) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) by MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2), MARK(tt)) MARK(U42(s(z0), x1, x2)) -> c26(A__U42(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U42(0, x1, x2)) -> c26(A__U42(0, x1, x2), MARK(0)) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2), MARK(tt)) MARK(U42(s(z0), x1, x2)) -> c26(A__U42(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U42(0, x1, x2)) -> c26(A__U42(0, x1, x2), MARK(0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2), MARK(tt)) MARK(U42(s(z0), x1, x2)) -> c26(A__U42(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U42(0, x1, x2)) -> c26(A__U42(0, x1, x2), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2 ---------------------------------------- (77) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U42(0, x1, x2)) -> c26(A__U42(0, x1, x2), MARK(0)) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2), MARK(tt)) MARK(U42(s(z0), x1, x2)) -> c26(A__U42(s(mark(z0)), x1, x2), MARK(s(z0))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2), MARK(tt)) MARK(U42(s(z0), x1, x2)) -> c26(A__U42(s(mark(z0)), x1, x2), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2 ---------------------------------------- (79) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (81) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) by MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, tt)) -> c27(A__PLUS(mark(x0), tt), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(tt)) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(0)) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, tt)) -> c27(A__PLUS(mark(x0), tt), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(tt)) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, tt)) -> c27(A__PLUS(mark(x0), tt), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(tt)) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2 ---------------------------------------- (83) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) by MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, tt)) -> c28(A__PLUS(mark(x0), tt), MARK(tt)) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, tt)) -> c28(A__PLUS(mark(x0), tt), MARK(tt)) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, tt)) -> c28(A__PLUS(mark(x0), tt), MARK(tt)) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2 ---------------------------------------- (87) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(x0, tt)) -> c28(A__PLUS(mark(x0), tt), MARK(tt)) ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2 ---------------------------------------- (89) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (91) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) by A__U41(tt, x0, plus(x1, z1)) -> c8(A__U42(U11(a__isNat(x1), z1), x0, plus(x1, z1)), A__ISNAT(plus(x1, z1))) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(x1, z1)) -> c8(A__U42(U11(a__isNat(x1), z1), x0, plus(x1, z1)), A__ISNAT(plus(x1, z1))) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(x1, z1)) -> c8(A__U42(U11(a__isNat(x1), z1), x0, plus(x1, z1)), A__ISNAT(plus(x1, z1))) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (93) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1 ---------------------------------------- (95) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) by A__U41(tt, x0, s(x1)) -> c8(A__U42(U21(a__isNat(x1)), x0, s(x1)), A__ISNAT(s(x1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(x1)) -> c8(A__U42(U21(a__isNat(x1)), x0, s(x1)), A__ISNAT(s(x1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(x1)) -> c8(A__U42(U21(a__isNat(x1)), x0, s(x1)), A__ISNAT(s(x1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (97) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (99) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) by A__U42(tt, U11(x0, z1), x2) -> c10(A__PLUS(mark(x2), U11(mark(x0), z1)), MARK(x2)) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(tt)) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)), MARK(0)) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(x0, z1), x2) -> c10(A__PLUS(mark(x2), U11(mark(x0), z1)), MARK(x2)) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(tt)) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)), MARK(0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(x0, z1), x2) -> c10(A__PLUS(mark(x2), U11(mark(x0), z1)), MARK(x2)) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(tt)) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (101) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (103) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) by A__U42(tt, U12(x0), x1) -> c10(A__PLUS(mark(x1), U12(mark(x0))), MARK(x1)) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0))), MARK(tt)) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0))), MARK(0)) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(x0), x1) -> c10(A__PLUS(mark(x1), U12(mark(x0))), MARK(x1)) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0))), MARK(tt)) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0))), MARK(0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(x0), x1) -> c10(A__PLUS(mark(x1), U12(mark(x0))), MARK(x1)) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0))), MARK(tt)) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0))), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (105) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (107) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) by A__U42(tt, isNat(0), x1) -> c10(A__PLUS(mark(x1), tt), MARK(x1)) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), isNat(z0)), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0)), MARK(tt)) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0)), MARK(0)) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(0), x1) -> c10(A__PLUS(mark(x1), tt), MARK(x1)) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), isNat(z0)), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0)), MARK(tt)) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0)), MARK(0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(0), x1) -> c10(A__PLUS(mark(x1), tt), MARK(x1)) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), isNat(z0)), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0)), MARK(tt)) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (109) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (111) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) by A__U42(tt, U21(x0), x1) -> c10(A__PLUS(mark(x1), U21(mark(x0))), MARK(x1)) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0))), MARK(tt)) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0))), MARK(0)) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(x0), x1) -> c10(A__PLUS(mark(x1), U21(mark(x0))), MARK(x1)) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0))), MARK(tt)) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0))), MARK(0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(x0), x1) -> c10(A__PLUS(mark(x1), U21(mark(x0))), MARK(x1)) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0))), MARK(tt)) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0))), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (113) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (115) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) by A__U42(tt, U31(x0, z1), x2) -> c10(A__PLUS(mark(x2), U31(mark(x0), z1)), MARK(x2)) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(tt)) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1)), MARK(0)) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(x0, z1), x2) -> c10(A__PLUS(mark(x2), U31(mark(x0), z1)), MARK(x2)) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(tt)) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1)), MARK(0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(x0, z1), x2) -> c10(A__PLUS(mark(x2), U31(mark(x0), z1)), MARK(x2)) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(tt)) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (117) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (119) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) by A__U42(tt, U41(x0, z1, z2), x3) -> c10(A__PLUS(mark(x3), U41(mark(x0), z1, z2)), MARK(x3)) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(tt)) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(0)) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), 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z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(A__PLUS(mark(x3), U41(mark(x0), z1, z2)), MARK(x3)) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(tt)) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(A__PLUS(mark(x3), U41(mark(x0), z1, z2)), MARK(x3)) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(tt)) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (121) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (123) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) by A__U42(tt, U42(x0, z1, z2), x3) -> c10(A__PLUS(mark(x3), U42(mark(x0), z1, z2)), MARK(x3)) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(tt)) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(0)) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(A__PLUS(mark(x3), U42(mark(x0), z1, z2)), MARK(x3)) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(tt)) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(A__PLUS(mark(x3), U42(mark(x0), z1, z2)), MARK(x3)) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(tt)) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (125) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), 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a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (127) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) by A__U42(tt, plus(x0, x1), x2) -> c10(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(x2)) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(tt)) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(0)) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), 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MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), 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a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(tt)) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, x1), x2) -> c10(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(x2)) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(tt)) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (129) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1)))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1)))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (131) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) by A__U42(tt, U11(z0, z1), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), a__U11(mark(z0), z1)), MARK(U11(x1, x2))) A__U42(tt, U12(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), a__U12(mark(z0))), MARK(U11(x1, x2))) A__U42(tt, isNat(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), a__isNat(z0)), MARK(U11(x1, x2))) A__U42(tt, U21(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), a__U21(mark(z0))), MARK(U11(x1, x2))) A__U42(tt, U31(z0, z1), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), a__U31(mark(z0), z1)), MARK(U11(x1, x2))) A__U42(tt, U41(z0, z1, z2), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), a__U41(mark(z0), z1, z2)), MARK(U11(x1, x2))) A__U42(tt, U42(z0, z1, z2), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), a__U42(mark(z0), z1, z2)), MARK(U11(x1, x2))) A__U42(tt, plus(z0, z1), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), a__plus(mark(z0), mark(z1))), MARK(U11(x1, x2))) A__U42(tt, tt, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), tt), MARK(U11(x1, x2))) A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2))) A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2))) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0)), MARK(U11(0, x2))) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, 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U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U42(tt, tt, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), tt), MARK(U11(x1, x2))) A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2))) A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2))) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0)), MARK(U11(0, x2))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U42(tt, tt, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), tt), MARK(U11(x1, x2))) A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2))) A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2))) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0)), MARK(U11(0, x2))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (133) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), 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c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2))) A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2))) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, 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U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2))) A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2))) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (135) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) by A__U42(tt, U11(z0, z1), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), a__U11(mark(z0), z1)), MARK(U12(x1))) A__U42(tt, U12(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), a__U12(mark(z0))), MARK(U12(x1))) A__U42(tt, isNat(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), a__isNat(z0)), MARK(U12(x1))) A__U42(tt, U21(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), a__U21(mark(z0))), MARK(U12(x1))) A__U42(tt, U31(z0, z1), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), a__U31(mark(z0), z1)), MARK(U12(x1))) A__U42(tt, U41(z0, z1, z2), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), a__U41(mark(z0), z1, z2)), MARK(U12(x1))) A__U42(tt, U42(z0, z1, z2), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), a__U42(mark(z0), z1, z2)), MARK(U12(x1))) A__U42(tt, plus(z0, z1), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), a__plus(mark(z0), mark(z1))), MARK(U12(x1))) A__U42(tt, tt, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), tt), MARK(U12(x1))) A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1))) A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1))) A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1))) A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1)))) A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0)))) A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2))) A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2))) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0))) A__U42(tt, tt, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), tt), MARK(U12(x1))) A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1))) A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1))) A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1))) A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1)))) A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0)))) A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2))) A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2))) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0))) A__U42(tt, tt, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), tt), MARK(U12(x1))) A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1))) A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1))) A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1))) A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1)))) A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0)))) A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (137) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) 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A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2))) A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2))) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0))) A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1))) A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1))) A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1))) A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1)))) A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0)))) A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, 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U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2))) A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2))) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0))) A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1))) A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1))) A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1))) A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1)))) A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0)))) A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (139) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) by A__U42(tt, U11(z0, z1), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), a__U11(mark(z0), z1)), MARK(isNat(x1))) A__U42(tt, U12(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), a__U12(mark(z0))), MARK(isNat(x1))) A__U42(tt, isNat(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), a__isNat(z0)), MARK(isNat(x1))) A__U42(tt, U21(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), a__U21(mark(z0))), MARK(isNat(x1))) A__U42(tt, U31(z0, z1), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), a__U31(mark(z0), z1)), MARK(isNat(x1))) A__U42(tt, U41(z0, z1, z2), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), a__U41(mark(z0), z1, z2)), MARK(isNat(x1))) A__U42(tt, U42(z0, z1, z2), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), a__U42(mark(z0), z1, z2)), MARK(isNat(x1))) A__U42(tt, plus(z0, z1), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), a__plus(mark(z0), mark(z1))), MARK(isNat(x1))) A__U42(tt, tt, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), tt), MARK(isNat(x1))) A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0)))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 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A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2))) A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2))) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0))) A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1))) A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1))) A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1))) A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1)))) A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0)))) A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), tt), MARK(isNat(x1))) A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0)))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2))) A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2))) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0))) A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1))) A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1))) A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1))) A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1)))) A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0)))) A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), tt), MARK(isNat(x1))) A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0)))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (141) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2))) A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2))) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0))) A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1))) A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1))) A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1))) A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1)))) A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0)))) A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0)))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, 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A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), 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A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2))) A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2))) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0))) A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1))) A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1))) A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1))) A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1)))) A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0)))) A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0)))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (143) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) by A__U42(tt, U11(z0, z1), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), a__U11(mark(z0), z1)), MARK(U21(x1))) A__U42(tt, U12(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), a__U12(mark(z0))), MARK(U21(x1))) A__U42(tt, isNat(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), a__isNat(z0)), MARK(U21(x1))) A__U42(tt, U21(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), a__U21(mark(z0))), MARK(U21(x1))) A__U42(tt, U31(z0, z1), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), a__U31(mark(z0), z1)), MARK(U21(x1))) A__U42(tt, U41(z0, z1, z2), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), a__U41(mark(z0), z1, z2)), MARK(U21(x1))) A__U42(tt, U42(z0, z1, z2), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), a__U42(mark(z0), z1, z2)), MARK(U21(x1))) A__U42(tt, plus(z0, z1), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), a__plus(mark(z0), mark(z1))), MARK(U21(x1))) A__U42(tt, tt, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), tt), MARK(U21(x1))) A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1))) A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1))) A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1))) A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1)))) A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0)))) A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0)))) A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0)))) A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1)))) A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1)))) A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt))) A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0)))) A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0))) A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1))) ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2))) A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2))) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0))) A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1))) A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1))) A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1))) A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1)))) A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0)))) A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0)))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1))) A__U42(tt, tt, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), tt), MARK(U21(x1))) A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1))) A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1))) A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1))) A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1)))) A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0)))) A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0)))) A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0)))) A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1)))) A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1)))) A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt))) A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0)))) A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0))) A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), 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c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2))) A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2))) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0))) A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1))) A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1))) A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1))) A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1)))) A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0)))) A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0)))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1))) A__U42(tt, tt, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), tt), MARK(U21(x1))) A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1))) A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1))) A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1))) A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1)))) A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0)))) A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0)))) A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0)))) A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1)))) A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1)))) A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt))) A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0)))) A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0))) A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (145) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, 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x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2))) A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2))) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0))) A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1))) A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1))) A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1))) A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1)))) A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0)))) A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0)))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1))) A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1))) A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1))) A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1))) A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1)))) A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0)))) A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0)))) A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0)))) A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1)))) A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1)))) A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt))) A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0)))) A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0))) A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), 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c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1))) A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1))) A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1))) A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1)))) A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0)))) A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0)))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1))) A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1))) A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1))) A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1))) A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1)))) A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0)))) A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0)))) A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0)))) A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1)))) A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1)))) A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt))) A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0)))) A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0))) A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (147) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) by A__U42(tt, U11(z0, z1), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), a__U11(mark(z0), z1)), MARK(U31(x1, x2))) A__U42(tt, U12(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), a__U12(mark(z0))), MARK(U31(x1, x2))) A__U42(tt, isNat(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), a__isNat(z0)), MARK(U31(x1, x2))) A__U42(tt, U21(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), a__U21(mark(z0))), MARK(U31(x1, x2))) A__U42(tt, U31(z0, z1), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), a__U31(mark(z0), z1)), MARK(U31(x1, x2))) A__U42(tt, U41(z0, z1, z2), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), a__U41(mark(z0), z1, z2)), MARK(U31(x1, x2))) A__U42(tt, U42(z0, z1, z2), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), a__U42(mark(z0), z1, z2)), MARK(U31(x1, x2))) A__U42(tt, plus(z0, z1), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), a__plus(mark(z0), mark(z1))), MARK(U31(x1, x2))) A__U42(tt, tt, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), tt), MARK(U31(x1, x2))) A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2))) A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2))) A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2))) A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2))) A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0)), MARK(U31(0, x2))) ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2))) A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2))) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0))) A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1))) A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1))) A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1))) A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1)))) A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0)))) A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0)))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1))) A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1))) A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1))) A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1))) A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1)))) A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0)))) A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0)))) A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0)))) A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1)))) A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1)))) A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt))) A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0)))) A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0))) A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, tt, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), tt), MARK(U31(x1, x2))) A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2))) A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2))) A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2))) A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2))) A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0)), MARK(U31(0, x2))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2))) A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2))) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0))) A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1))) A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1))) A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1))) A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1)))) A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0)))) A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0)))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1))) A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1))) A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1))) A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1))) A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1)))) A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0)))) A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0)))) A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0)))) A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1)))) A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1)))) A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt))) A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0)))) A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0))) A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, tt, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), tt), MARK(U31(x1, x2))) A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2))) A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2))) A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2))) A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2))) A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0)), MARK(U31(0, x2))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (149) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), 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a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2))) A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2))) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0))) A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1))) A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1))) A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1))) A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1)))) A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0)))) A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0)))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1))) A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1))) A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1))) A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1))) A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1)))) A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0)))) A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0)))) A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0)))) A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1)))) A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1)))) A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt))) A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0)))) A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0))) A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2))) A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2))) A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2))) A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2))) A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2))) A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2))) A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2))) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0))) A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1))) A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1))) A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1))) A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1)))) A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0)))) A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0)))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1))) A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1))) A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1))) A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1))) A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1)))) A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0)))) A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0)))) A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0)))) A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1)))) A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1)))) A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt))) A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0)))) A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0))) A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2))) A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2))) A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2))) A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2))) A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2))) A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (151) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) by A__U42(tt, U11(z0, z1), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), a__U11(mark(z0), z1)), MARK(U41(x1, x2, x3))) A__U42(tt, U12(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), a__U12(mark(z0))), MARK(U41(x1, x2, x3))) A__U42(tt, isNat(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), a__isNat(z0)), MARK(U41(x1, x2, x3))) A__U42(tt, U21(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), a__U21(mark(z0))), MARK(U41(x1, x2, x3))) A__U42(tt, U31(z0, z1), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), a__U31(mark(z0), z1)), MARK(U41(x1, x2, x3))) A__U42(tt, U41(z0, z1, z2), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), a__U41(mark(z0), z1, z2)), MARK(U41(x1, x2, x3))) A__U42(tt, U42(z0, z1, z2), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), a__U42(mark(z0), z1, z2)), MARK(U41(x1, x2, x3))) A__U42(tt, plus(z0, z1), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), a__plus(mark(z0), mark(z1))), MARK(U41(x1, x2, x3))) A__U42(tt, tt, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), tt), MARK(U41(x1, x2, x3))) A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3))) A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3))) A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3))) A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0)), MARK(U41(0, x2, x3))) ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) 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MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2))) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0))) A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1))) A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1))) A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1))) A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1)))) A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0)))) A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0)))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1))) A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1))) A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1))) A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1))) A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1)))) A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0)))) A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0)))) A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0)))) A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1)))) A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1)))) A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt))) A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0)))) A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0))) A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2))) A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2))) A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2))) A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2))) A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2))) A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0))) A__U42(tt, tt, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), tt), MARK(U41(x1, x2, x3))) A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3))) A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3))) A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3))) A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0)), MARK(U41(0, x2, x3))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2))) A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2))) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0))) A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1))) A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1))) A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1))) A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1)))) A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0)))) A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0)))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1))) A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1))) A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1))) A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1))) A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1)))) A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0)))) A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0)))) A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0)))) A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1)))) A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1)))) A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt))) A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0)))) A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0))) A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2))) A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2))) A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2))) A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2))) A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2))) A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0))) A__U42(tt, tt, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), tt), MARK(U41(x1, x2, x3))) A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3))) A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3))) A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3))) A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0)), MARK(U41(0, x2, x3))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (153) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, 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A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2))) A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2))) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0))) A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1))) A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1))) A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1))) A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1)))) A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0)))) A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0)))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1))) A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1))) A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1))) A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1))) A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1)))) A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0)))) A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0)))) A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0)))) A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1)))) A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1)))) A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt))) A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0)))) A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0))) A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2))) A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2))) A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2))) A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2))) A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2))) A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0))) A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3))) A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3))) A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3))) A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> 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MARK(U31(plus(z0, z1), x2))) A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2))) A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0))) A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3))) A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3))) A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3))) A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (155) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) by A__U42(tt, U11(z0, z1), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), a__U11(mark(z0), z1)), MARK(U42(x1, x2, x3))) A__U42(tt, U12(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), a__U12(mark(z0))), MARK(U42(x1, x2, x3))) A__U42(tt, isNat(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), a__isNat(z0)), MARK(U42(x1, x2, x3))) A__U42(tt, U21(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), a__U21(mark(z0))), MARK(U42(x1, x2, x3))) A__U42(tt, U31(z0, z1), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), a__U31(mark(z0), z1)), MARK(U42(x1, x2, x3))) A__U42(tt, U41(z0, z1, z2), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), a__U41(mark(z0), z1, z2)), MARK(U42(x1, x2, x3))) A__U42(tt, U42(z0, z1, z2), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), a__U42(mark(z0), z1, z2)), MARK(U42(x1, x2, x3))) A__U42(tt, plus(z0, z1), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), a__plus(mark(z0), mark(z1))), MARK(U42(x1, x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), tt), MARK(U42(x1, x2, x3))) A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3))) A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2))) A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3))) A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3))) A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3))) A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3))) A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3))) A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0)), MARK(U42(0, x2, x3))) ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> 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z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), tt), MARK(U42(x1, x2, x3))) A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3))) A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2))) A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3))) A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3))) A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3))) A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3))) A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3))) A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0)), MARK(U42(0, x2, x3))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, 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A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> 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A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2))) A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2))) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0))) A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1))) A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1))) A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1))) A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1)))) A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0)))) A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0)))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1))) A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1))) A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1))) A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1))) A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1)))) A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0)))) A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0)))) A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0)))) A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1)))) A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1)))) A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt))) A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0)))) A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0))) A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2))) A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2))) A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2))) A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2))) A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2))) A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0))) A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3))) A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3))) A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3))) A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), tt), MARK(U42(x1, x2, x3))) A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3))) A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2))) A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3))) A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3))) A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3))) A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3))) A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3))) A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0)), MARK(U42(0, x2, x3))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (157) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), 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mark(x0)), MARK(U31(x1, z1))) A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2))) A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2))) A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2))) A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2))) A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2))) A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0))) A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3))) A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3))) A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3))) A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3))) A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2))) A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3))) A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3))) A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3))) A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3))) A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3))) A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> 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z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3))) A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2))) A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3))) A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3))) A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3))) A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3))) A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3))) A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (159) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) by A__U42(tt, U11(z0, z1), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), a__U11(mark(z0), z1)), MARK(plus(x1, x2))) A__U42(tt, U12(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), a__U12(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, isNat(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), a__isNat(z0)), MARK(plus(x1, x2))) A__U42(tt, U21(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), a__U21(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, U31(z0, z1), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), a__U31(mark(z0), z1)), MARK(plus(x1, x2))) A__U42(tt, U41(z0, z1, z2), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), a__U41(mark(z0), z1, z2)), MARK(plus(x1, x2))) A__U42(tt, U42(z0, z1, z2), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), a__U42(mark(z0), z1, z2)), MARK(plus(x1, x2))) A__U42(tt, plus(z0, z1), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), a__plus(mark(z0), mark(z1))), MARK(plus(x1, x2))) A__U42(tt, tt, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(plus(x1, x2))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0)))) A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2)))) A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2))) A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2))) A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2))) A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, 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A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0))) A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3))) A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3))) A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3))) A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3))) A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2))) A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3))) A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3))) A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3))) A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3))) A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3))) A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) A__U42(tt, tt, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(plus(x1, x2))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0)))) A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2)))) A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2))) A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2))) A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2))) A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, 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x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3))) A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2))) A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3))) A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3))) A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3))) A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3))) A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3))) A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) A__U42(tt, tt, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(plus(x1, x2))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0)))) A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2)))) A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2))) A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2))) A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2))) A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (161) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), 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MARK(U42(x1, z1, z2))) A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3))) A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3))) A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3))) A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3))) A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3))) A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0)))) A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2)))) A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2))) A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2))) A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2))) A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), 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c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2))) A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2))) A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2))) A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, 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x2, x3), mark(x0))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0)))) A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2)))) A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2))) A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2))) A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2))) A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (163) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) by A__U42(tt, U11(z0, z1), s(x1)) -> c10(A__PLUS(s(mark(x1)), a__U11(mark(z0), z1)), MARK(s(x1))) A__U42(tt, U12(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), a__U12(mark(z0))), MARK(s(x1))) A__U42(tt, isNat(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), a__isNat(z0)), MARK(s(x1))) A__U42(tt, U21(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), a__U21(mark(z0))), MARK(s(x1))) A__U42(tt, U31(z0, z1), s(x1)) -> c10(A__PLUS(s(mark(x1)), a__U31(mark(z0), z1)), MARK(s(x1))) A__U42(tt, U41(z0, z1, z2), s(x1)) -> c10(A__PLUS(s(mark(x1)), a__U41(mark(z0), z1, z2)), MARK(s(x1))) A__U42(tt, U42(z0, z1, z2), s(x1)) -> c10(A__PLUS(s(mark(x1)), a__U42(mark(z0), z1, z2)), MARK(s(x1))) A__U42(tt, plus(z0, z1), s(x1)) -> c10(A__PLUS(s(mark(x1)), a__plus(mark(z0), mark(z1))), MARK(s(x1))) A__U42(tt, tt, s(x1)) -> c10(A__PLUS(s(mark(x1)), tt), MARK(s(x1))) A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0)))) A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0)))) A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1)))) A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2)))) A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2)))) A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1))) ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), 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c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3))) A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3))) A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3))) A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3))) A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0)))) A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2)))) A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2))) A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2))) A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2))) A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2))) A__U42(tt, tt, s(x1)) -> c10(A__PLUS(s(mark(x1)), tt), MARK(s(x1))) A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0)))) A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0)))) A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1)))) A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2)))) A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2)))) A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> 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c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2))) A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2))) A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2))) A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, 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x2, x3), mark(x0))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0)))) A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2)))) A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2))) A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2))) A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2))) A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2))) A__U42(tt, tt, s(x1)) -> c10(A__PLUS(s(mark(x1)), tt), MARK(s(x1))) A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0)))) A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0)))) A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1)))) A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2)))) A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2)))) A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (165) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), 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z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0)))) A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2)))) A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2))) A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2))) A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2))) A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2))) A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0)))) A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0)))) A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1)))) A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2)))) A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2)))) A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), 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mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0)))) A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2)))) A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2))) A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2))) A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2))) A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2))) A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0)))) A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0)))) A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1)))) A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2)))) A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2)))) A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (167) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) by A__U42(tt, U11(z0, z1), tt) -> c10(A__PLUS(tt, a__U11(mark(z0), z1))) A__U42(tt, U12(z0), tt) -> c10(A__PLUS(tt, a__U12(mark(z0)))) A__U42(tt, isNat(z0), tt) -> c10(A__PLUS(tt, a__isNat(z0))) A__U42(tt, U21(z0), tt) -> c10(A__PLUS(tt, a__U21(mark(z0)))) A__U42(tt, U31(z0, z1), tt) -> c10(A__PLUS(tt, a__U31(mark(z0), z1))) A__U42(tt, U41(z0, z1, z2), tt) -> c10(A__PLUS(tt, a__U41(mark(z0), z1, z2))) A__U42(tt, U42(z0, z1, z2), tt) -> c10(A__PLUS(tt, a__U42(mark(z0), z1, z2))) A__U42(tt, plus(z0, z1), tt) -> c10(A__PLUS(tt, a__plus(mark(z0), mark(z1)))) A__U42(tt, tt, tt) -> c10(A__PLUS(tt, tt)) A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0)))) A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0)) ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), 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c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3))) A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3))) A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3))) A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3))) A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0)))) A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2)))) A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2))) A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2))) A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2))) A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2))) A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0)))) A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0)))) A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1)))) A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2)))) A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2)))) A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, tt, tt) -> c10(A__PLUS(tt, tt)) A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0)))) A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), 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A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0))) A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1))) A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1))) A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1))) A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1)))) A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0)))) A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0)))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1))) A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1))) A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1))) A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1))) A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1)))) A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0)))) A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0)))) A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0)))) A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1)))) A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1)))) A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt))) A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0)))) A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0))) A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2))) A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2))) A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2))) A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2))) A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2))) A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0))) A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3))) A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3))) A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3))) A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3))) A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2))) A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3))) A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3))) A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3))) A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3))) A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3))) A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0)))) A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2)))) A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2))) A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2))) A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2))) A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2))) A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0)))) A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0)))) A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1)))) A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2)))) A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2)))) A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, tt, tt) -> c10(A__PLUS(tt, tt)) A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0)))) A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (169) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U42(tt, tt, tt) -> c10(A__PLUS(tt, tt)) ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, 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z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0)))) A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2)))) A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2))) A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2))) A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2))) A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2))) A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0)))) A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0)))) A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1)))) A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2)))) A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2)))) A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0)))) A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, 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mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0)))) A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2)))) A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2))) A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2))) A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2))) A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2))) A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0)))) A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0)))) A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1)))) A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2)))) A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2)))) A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0)))) A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (171) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) by A__U42(tt, U11(z0, z1), 0) -> c10(A__PLUS(0, a__U11(mark(z0), z1))) A__U42(tt, U12(z0), 0) -> c10(A__PLUS(0, a__U12(mark(z0)))) A__U42(tt, isNat(z0), 0) -> c10(A__PLUS(0, a__isNat(z0))) A__U42(tt, U21(z0), 0) -> c10(A__PLUS(0, a__U21(mark(z0)))) A__U42(tt, U31(z0, z1), 0) -> c10(A__PLUS(0, a__U31(mark(z0), z1))) A__U42(tt, U41(z0, z1, z2), 0) -> c10(A__PLUS(0, a__U41(mark(z0), z1, z2))) A__U42(tt, U42(z0, z1, z2), 0) -> c10(A__PLUS(0, a__U42(mark(z0), z1, z2))) A__U42(tt, plus(z0, z1), 0) -> c10(A__PLUS(0, a__plus(mark(z0), mark(z1)))) A__U42(tt, tt, 0) -> c10(A__PLUS(0, tt)) A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0)))) A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0)) ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), 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A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, 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c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2))) A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3))) A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3))) A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3))) A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3))) A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3))) A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0)))) A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2)))) A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2))) A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2))) A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2))) A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2))) A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0)))) A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0)))) A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1)))) A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2)))) A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2)))) A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0)))) A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0)) A__U42(tt, tt, 0) -> c10(A__PLUS(0, tt)) A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0)))) A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), 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z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0)))) A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2)))) A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2))) A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2))) A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2))) A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2))) A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0)))) A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0)))) A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1)))) A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2)))) A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2)))) A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0)))) A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0)) A__U42(tt, tt, 0) -> c10(A__PLUS(0, tt)) A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0)))) A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (173) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U42(tt, tt, 0) -> c10(A__PLUS(0, tt)) ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), 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MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), 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MARK(U41(tt, x2, x3))) A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3))) A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2))) A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3))) A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3))) A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3))) A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3))) A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3))) A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0)))) A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2)))) A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2))) A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2))) A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2))) A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2))) A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0)))) A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0)))) A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1)))) A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2)))) A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2)))) A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0)))) A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0)) A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0)))) A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), 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c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0)))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1))) A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1))) A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1))) A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1))) A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1)))) A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0)))) A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0)))) A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0)))) A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1)))) A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1)))) A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt))) A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0)))) A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0))) A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2))) A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2))) A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2))) A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2))) A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2))) A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0))) A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3))) A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3))) A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3))) A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3))) A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2))) A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3))) A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3))) A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3))) A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3))) A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3))) A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0)))) A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2)))) A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2))) A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2))) A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2))) A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2))) A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0)))) A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0)))) A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1)))) A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2)))) A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2)))) A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0)))) A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0)) A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0)))) A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (175) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) by A__U42(tt, U11(x0, z1), x2) -> c11(A__PLUS(mark(x2), U11(mark(x0), z1)), MARK(U11(x0, z1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1))) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1))) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1)), MARK(U11(0, x1))) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, 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a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1))) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1))) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1)), MARK(U11(0, x1))) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> 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MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2))) A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0)))) A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0)))) A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1)))) A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2)))) A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2)))) A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0)))) A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0)) A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0)))) A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0)) A__U42(tt, U11(x0, z1), x2) -> c11(A__PLUS(mark(x2), U11(mark(x0), z1)), MARK(U11(x0, z1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1))) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1))) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1)), MARK(U11(0, x1))) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (177) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), 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MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0)))) A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2)))) A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2))) A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2))) A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2))) A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2))) A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0)))) A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0)))) A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1)))) A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2)))) A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2)))) A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0)))) A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0)) A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0)))) A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0)) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1))) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1))) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, z1), x2) -> c11(MARK(U11(x0, z1))) A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> 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MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), 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a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), 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c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2))) A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3))) A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3))) A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3))) A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3))) A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3))) A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0)))) A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2)))) A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2))) A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2))) A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2))) A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2))) A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0)))) A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0)))) A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1)))) A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2)))) A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2)))) A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0)))) A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0)) A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0)))) A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0)) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1))) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1))) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, z1), x2) -> c11(MARK(U11(x0, z1))) A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (179) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) by A__U42(tt, U12(x0), x1) -> c11(A__PLUS(mark(x1), U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U42(tt, U12(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U42(tt, U12(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U42(tt, U12(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(U12(U21(z0)))) A__U42(tt, U12(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, U12(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(U12(plus(z0, z1)))) A__U42(tt, U12(tt), x1) -> c11(A__PLUS(mark(x1), a__U12(tt)), MARK(U12(tt))) A__U42(tt, U12(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U42(tt, U12(0), x1) -> c11(A__PLUS(mark(x1), a__U12(0)), MARK(U12(0))) A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0))) ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2))) A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2))) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0))) A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1))) A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1))) A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1))) A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1)))) A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0)))) A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0)))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1))) A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1))) A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1))) A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1))) A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1)))) A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0)))) A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0)))) A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0)))) A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1)))) A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1)))) A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt))) A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0)))) A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0))) A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2))) A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2))) A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2))) A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2))) A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2))) A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0))) A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3))) A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3))) A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3))) A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3))) A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2))) A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3))) A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3))) A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3))) A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3))) A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3))) A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0)))) A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2)))) A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2))) A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2))) A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2))) A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2))) A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0)))) A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0)))) A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1)))) A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2)))) A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2)))) A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0)))) A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0)) A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0)))) A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0)) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1))) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1))) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, z1), x2) -> c11(MARK(U11(x0, z1))) A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1))) A__U42(tt, U12(x0), x1) -> c11(A__PLUS(mark(x1), U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U42(tt, U12(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U42(tt, U12(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U42(tt, U12(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(U12(U21(z0)))) A__U42(tt, U12(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, U12(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(U12(plus(z0, z1)))) A__U42(tt, U12(tt), x1) -> c11(A__PLUS(mark(x1), a__U12(tt)), MARK(U12(tt))) A__U42(tt, U12(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U42(tt, U12(0), x1) -> c11(A__PLUS(mark(x1), a__U12(0)), MARK(U12(0))) A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), 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MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0)))) A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2)))) A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2))) A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2))) A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2))) A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2))) A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0)))) A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0)))) A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1)))) A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2)))) A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2)))) A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0)))) A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0)) A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0)))) A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0)) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1))) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1))) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, z1), x2) -> c11(MARK(U11(x0, z1))) A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1))) A__U42(tt, U12(x0), x1) -> c11(A__PLUS(mark(x1), U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U42(tt, U12(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U42(tt, U12(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U42(tt, U12(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(U12(U21(z0)))) A__U42(tt, U12(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, U12(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(U12(plus(z0, z1)))) A__U42(tt, U12(tt), x1) -> c11(A__PLUS(mark(x1), a__U12(tt)), MARK(U12(tt))) A__U42(tt, U12(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U42(tt, U12(0), x1) -> c11(A__PLUS(mark(x1), a__U12(0)), MARK(U12(0))) A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (181) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (182) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, 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z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, z1), x2) -> c11(MARK(U11(x0, z1))) A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U42(tt, U12(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U42(tt, U12(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U42(tt, U12(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(U12(U21(z0)))) A__U42(tt, U12(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, U12(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(U12(plus(z0, z1)))) A__U42(tt, U12(tt), x1) -> c11(A__PLUS(mark(x1), a__U12(tt)), MARK(U12(tt))) A__U42(tt, U12(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U42(tt, U12(0), x1) -> c11(A__PLUS(mark(x1), a__U12(0)), MARK(U12(0))) A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) 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z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), 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z1)), mark(x0)), MARK(U21(U31(z0, z1)))) A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1)))) A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt))) A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0)))) A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0))) A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2))) A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2))) A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2))) A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2))) A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2))) A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0))) A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3))) A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3))) A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3))) A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3))) A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2))) A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3))) A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3))) A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3))) A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3))) A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3))) A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, 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plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2)))) A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2))) A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2))) A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2))) A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2))) A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0)))) A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0)))) A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1)))) A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2)))) A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2)))) A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0)))) A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0)) A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0)))) A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0)) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1))) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1))) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, z1), x2) -> c11(MARK(U11(x0, z1))) A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U42(tt, U12(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U42(tt, U12(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U42(tt, U12(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(U12(U21(z0)))) A__U42(tt, U12(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, U12(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(U12(plus(z0, z1)))) A__U42(tt, U12(tt), x1) -> c11(A__PLUS(mark(x1), a__U12(tt)), MARK(U12(tt))) A__U42(tt, U12(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U42(tt, U12(0), x1) -> c11(A__PLUS(mark(x1), a__U12(0)), MARK(U12(0))) A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (183) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) by A__U42(tt, isNat(0), x1) -> c11(A__PLUS(mark(x1), tt), MARK(isNat(0))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(isNat(plus(z0, z1)))) A__U42(tt, isNat(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(isNat(s(z0)))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), isNat(z0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) ---------------------------------------- (184) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), 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x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2))) A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2))) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0))) A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1))) A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1))) A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1))) A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1)))) A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0)))) A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0)))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1))) A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1))) A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1))) A__U42(tt, x0, U21(x1)) -> 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A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0)))) A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0)) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1))) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1))) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, z1), x2) -> c11(MARK(U11(x0, z1))) A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U42(tt, U12(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U42(tt, U12(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U42(tt, U12(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(U12(U21(z0)))) A__U42(tt, U12(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, U12(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(U12(plus(z0, z1)))) A__U42(tt, U12(tt), x1) -> c11(A__PLUS(mark(x1), a__U12(tt)), MARK(U12(tt))) A__U42(tt, U12(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U42(tt, U12(0), x1) -> c11(A__PLUS(mark(x1), a__U12(0)), MARK(U12(0))) A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0))) A__U42(tt, isNat(0), x1) -> c11(A__PLUS(mark(x1), tt), MARK(isNat(0))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(isNat(plus(z0, z1)))) A__U42(tt, isNat(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(isNat(s(z0)))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), isNat(z0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), 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c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3))) A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3))) A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3))) A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3))) A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0)))) A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2)))) A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2))) A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2))) A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2))) A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2))) A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0)))) A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0)))) A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1)))) A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2)))) A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2)))) A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0)))) A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0)) A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0)))) A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0)) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1))) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1))) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, z1), x2) -> c11(MARK(U11(x0, z1))) A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U42(tt, U12(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U42(tt, U12(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U42(tt, U12(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(U12(U21(z0)))) A__U42(tt, U12(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, U12(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(U12(plus(z0, z1)))) A__U42(tt, U12(tt), x1) -> c11(A__PLUS(mark(x1), a__U12(tt)), MARK(U12(tt))) A__U42(tt, U12(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U42(tt, U12(0), x1) -> c11(A__PLUS(mark(x1), a__U12(0)), MARK(U12(0))) A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0))) A__U42(tt, isNat(0), x1) -> c11(A__PLUS(mark(x1), tt), MARK(isNat(0))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(isNat(plus(z0, z1)))) A__U42(tt, isNat(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(isNat(s(z0)))) A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), isNat(z0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (185) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (186) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) 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-> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, 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x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), 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U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2))) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0))) A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1))) A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1))) A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1))) A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1)))) A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0)))) A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) 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s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0)))) A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0)))) A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1)))) A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2)))) A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2)))) A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0)))) A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0)) A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0)))) A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0)) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1))) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1))) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, z1), x2) -> c11(MARK(U11(x0, z1))) A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U42(tt, U12(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U42(tt, U12(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U42(tt, U12(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(U12(U21(z0)))) A__U42(tt, U12(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, U12(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(U12(plus(z0, z1)))) A__U42(tt, U12(tt), x1) -> c11(A__PLUS(mark(x1), a__U12(tt)), MARK(U12(tt))) A__U42(tt, U12(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U42(tt, U12(0), x1) -> c11(A__PLUS(mark(x1), a__U12(0)), MARK(U12(0))) A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(isNat(plus(z0, z1)))) A__U42(tt, isNat(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(isNat(s(z0)))) A__U42(tt, isNat(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(0), x1) -> c11(MARK(isNat(0))) A__U42(tt, isNat(z0), x1) -> c11(MARK(isNat(z0))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), 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mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3))) A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2))) A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3))) A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3))) A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3))) A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3))) A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3))) A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0)))) A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2)))) A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2))) A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2))) A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2))) A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2))) A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0)))) A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0)))) A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1)))) A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2)))) A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2)))) A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0)))) A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0)) A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0)))) A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0)) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1))) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1))) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, z1), x2) -> c11(MARK(U11(x0, z1))) A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U42(tt, U12(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U42(tt, U12(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U42(tt, U12(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(U12(U21(z0)))) A__U42(tt, U12(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, U12(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(U12(plus(z0, z1)))) A__U42(tt, U12(tt), x1) -> c11(A__PLUS(mark(x1), a__U12(tt)), MARK(U12(tt))) A__U42(tt, U12(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U42(tt, U12(0), x1) -> c11(A__PLUS(mark(x1), a__U12(0)), MARK(U12(0))) A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(isNat(plus(z0, z1)))) A__U42(tt, isNat(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(isNat(s(z0)))) A__U42(tt, isNat(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(0), x1) -> c11(MARK(isNat(0))) A__U42(tt, isNat(z0), x1) -> c11(MARK(isNat(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (187) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) by A__U42(tt, U21(x0), x1) -> c11(A__PLUS(mark(x1), U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(U21(U11(z0, z1)))) A__U42(tt, U21(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(U21(U12(z0)))) A__U42(tt, U21(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U42(tt, U21(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U42(tt, U21(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(U21(U31(z0, z1)))) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, U21(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(U21(plus(z0, z1)))) A__U42(tt, U21(tt), x1) -> c11(A__PLUS(mark(x1), a__U21(tt)), MARK(U21(tt))) A__U42(tt, U21(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U42(tt, U21(0), x1) -> c11(A__PLUS(mark(x1), a__U21(0)), MARK(U21(0))) A__U42(tt, U21(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0))) ---------------------------------------- (188) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, 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U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U42(tt, s(z0), U11(x1, x2)) -> 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MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2))) A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0)))) A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0)))) A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1)))) A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2)))) A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2)))) A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0)))) A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0)) A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0)))) A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0)) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1))) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1))) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, z1), x2) -> c11(MARK(U11(x0, z1))) A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U42(tt, U12(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U42(tt, U12(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U42(tt, U12(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(U12(U21(z0)))) A__U42(tt, U12(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, U12(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(U12(plus(z0, z1)))) A__U42(tt, U12(tt), x1) -> c11(A__PLUS(mark(x1), a__U12(tt)), MARK(U12(tt))) A__U42(tt, U12(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U42(tt, U12(0), x1) -> c11(A__PLUS(mark(x1), a__U12(0)), MARK(U12(0))) A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(isNat(plus(z0, z1)))) A__U42(tt, isNat(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(isNat(s(z0)))) A__U42(tt, isNat(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(0), x1) -> c11(MARK(isNat(0))) A__U42(tt, isNat(z0), x1) -> c11(MARK(isNat(z0))) A__U42(tt, U21(x0), x1) -> c11(A__PLUS(mark(x1), U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(U21(U11(z0, z1)))) A__U42(tt, U21(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(U21(U12(z0)))) A__U42(tt, U21(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U42(tt, U21(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U42(tt, U21(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(U21(U31(z0, z1)))) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, U21(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(U21(plus(z0, z1)))) A__U42(tt, U21(tt), x1) -> c11(A__PLUS(mark(x1), a__U21(tt)), MARK(U21(tt))) A__U42(tt, U21(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U42(tt, U21(0), x1) -> c11(A__PLUS(mark(x1), a__U21(0)), MARK(U21(0))) A__U42(tt, U21(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, 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U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1))) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1))) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, z1), x2) -> c11(MARK(U11(x0, z1))) A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U42(tt, U12(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U42(tt, U12(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U42(tt, U12(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(U12(U21(z0)))) A__U42(tt, U12(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, U12(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(U12(plus(z0, z1)))) A__U42(tt, U12(tt), x1) -> c11(A__PLUS(mark(x1), a__U12(tt)), MARK(U12(tt))) A__U42(tt, U12(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U42(tt, U12(0), x1) -> c11(A__PLUS(mark(x1), a__U12(0)), MARK(U12(0))) A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(isNat(plus(z0, z1)))) A__U42(tt, isNat(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(isNat(s(z0)))) A__U42(tt, isNat(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(0), x1) -> c11(MARK(isNat(0))) A__U42(tt, isNat(z0), x1) -> c11(MARK(isNat(z0))) A__U42(tt, U21(x0), x1) -> c11(A__PLUS(mark(x1), U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(U21(U11(z0, z1)))) A__U42(tt, U21(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(U21(U12(z0)))) A__U42(tt, U21(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U42(tt, U21(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U42(tt, U21(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(U21(U31(z0, z1)))) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, U21(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(U21(plus(z0, z1)))) A__U42(tt, U21(tt), x1) -> c11(A__PLUS(mark(x1), a__U21(tt)), MARK(U21(tt))) A__U42(tt, U21(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U42(tt, U21(0), x1) -> c11(A__PLUS(mark(x1), a__U21(0)), MARK(U21(0))) A__U42(tt, U21(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (189) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (190) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, 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c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, z1), x2) -> c11(MARK(U11(x0, z1))) A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U42(tt, U12(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U42(tt, U12(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U42(tt, U12(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(U12(U21(z0)))) A__U42(tt, U12(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, U12(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(U12(plus(z0, z1)))) A__U42(tt, U12(tt), x1) -> c11(A__PLUS(mark(x1), a__U12(tt)), MARK(U12(tt))) A__U42(tt, U12(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U42(tt, U12(0), x1) -> c11(A__PLUS(mark(x1), a__U12(0)), MARK(U12(0))) A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(isNat(plus(z0, z1)))) A__U42(tt, isNat(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(isNat(s(z0)))) A__U42(tt, isNat(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(0), x1) -> c11(MARK(isNat(0))) A__U42(tt, isNat(z0), x1) -> c11(MARK(isNat(z0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(U21(U11(z0, z1)))) A__U42(tt, U21(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(U21(U12(z0)))) A__U42(tt, U21(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U42(tt, U21(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U42(tt, U21(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(U21(U31(z0, z1)))) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, U21(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(U21(plus(z0, z1)))) A__U42(tt, U21(tt), x1) -> c11(A__PLUS(mark(x1), a__U21(tt)), MARK(U21(tt))) A__U42(tt, U21(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U42(tt, U21(0), x1) -> c11(A__PLUS(mark(x1), a__U21(0)), MARK(U21(0))) A__U42(tt, U21(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), 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c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(0), x1) -> c11(MARK(isNat(0))) A__U42(tt, isNat(z0), x1) -> c11(MARK(isNat(z0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(U21(U11(z0, z1)))) A__U42(tt, U21(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(U21(U12(z0)))) A__U42(tt, U21(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U42(tt, U21(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U42(tt, U21(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(U21(U31(z0, z1)))) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, U21(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(U21(plus(z0, z1)))) A__U42(tt, U21(tt), x1) -> c11(A__PLUS(mark(x1), a__U21(tt)), MARK(U21(tt))) A__U42(tt, U21(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U42(tt, U21(0), x1) -> c11(A__PLUS(mark(x1), a__U21(0)), MARK(U21(0))) A__U42(tt, U21(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (191) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) by A__U42(tt, U31(x0, z1), x2) -> c11(A__PLUS(mark(x2), U31(mark(x0), z1)), MARK(U31(x0, z1))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1))) A__U42(tt, U31(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1))) A__U42(tt, U31(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1))) A__U42(tt, U31(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(U31(U21(z0), x1))) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1))) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1))) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(U31(U42(z0, z1, z2), x1))) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(U31(plus(z0, z1), x1))) A__U42(tt, U31(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(U31(tt, x1))) A__U42(tt, U31(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1)), MARK(U31(0, x1))) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) ---------------------------------------- (192) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, 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a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), 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c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2))) A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2))) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0))) A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1))) A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1))) A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1))) A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1)))) A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0)))) A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0)))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1))) A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1))) A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1))) A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1))) A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1)))) A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0)))) A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0)))) A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0)))) A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1)))) A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1)))) A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt))) A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0)))) A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0))) A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2))) A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2))) A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2))) A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2))) A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2))) A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0))) A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3))) A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3))) A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3))) A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> 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U21(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(U21(U11(z0, z1)))) A__U42(tt, U21(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(U21(U12(z0)))) A__U42(tt, U21(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U42(tt, U21(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U42(tt, U21(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(U21(U31(z0, z1)))) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, U21(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(U21(plus(z0, z1)))) A__U42(tt, U21(tt), x1) -> c11(A__PLUS(mark(x1), a__U21(tt)), MARK(U21(tt))) A__U42(tt, U21(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U42(tt, U21(0), x1) -> c11(A__PLUS(mark(x1), a__U21(0)), MARK(U21(0))) A__U42(tt, U21(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0))) A__U42(tt, U31(x0, z1), x2) -> c11(A__PLUS(mark(x2), U31(mark(x0), z1)), MARK(U31(x0, z1))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1))) A__U42(tt, U31(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1))) A__U42(tt, U31(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1))) A__U42(tt, U31(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(U31(U21(z0), x1))) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1))) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1))) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(U31(U42(z0, z1, z2), x1))) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(U31(plus(z0, z1), x1))) A__U42(tt, U31(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(U31(tt, x1))) A__U42(tt, U31(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1)), MARK(U31(0, x1))) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), 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A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, 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c11(MARK(U12(x0))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(isNat(plus(z0, z1)))) A__U42(tt, isNat(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(isNat(s(z0)))) A__U42(tt, isNat(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(0), x1) -> c11(MARK(isNat(0))) A__U42(tt, isNat(z0), x1) -> c11(MARK(isNat(z0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(U21(U11(z0, z1)))) A__U42(tt, U21(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(U21(U12(z0)))) A__U42(tt, U21(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U42(tt, U21(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U42(tt, U21(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(U21(U31(z0, z1)))) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, U21(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(U21(plus(z0, z1)))) A__U42(tt, U21(tt), x1) -> c11(A__PLUS(mark(x1), a__U21(tt)), MARK(U21(tt))) A__U42(tt, U21(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U42(tt, U21(0), x1) -> c11(A__PLUS(mark(x1), a__U21(0)), MARK(U21(0))) A__U42(tt, U21(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0))) A__U42(tt, U31(x0, z1), x2) -> c11(A__PLUS(mark(x2), U31(mark(x0), z1)), MARK(U31(x0, z1))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1))) A__U42(tt, U31(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1))) A__U42(tt, U31(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1))) A__U42(tt, U31(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(U31(U21(z0), x1))) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1))) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1))) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(U31(U42(z0, z1, z2), x1))) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(U31(plus(z0, z1), x1))) A__U42(tt, U31(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(U31(tt, x1))) A__U42(tt, U31(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1)), MARK(U31(0, x1))) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (193) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (194) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), 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A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(isNat(plus(z0, z1)))) A__U42(tt, isNat(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(isNat(s(z0)))) A__U42(tt, isNat(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(0), x1) -> c11(MARK(isNat(0))) A__U42(tt, isNat(z0), x1) -> c11(MARK(isNat(z0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(U21(U11(z0, z1)))) A__U42(tt, U21(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(U21(U12(z0)))) A__U42(tt, U21(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U42(tt, U21(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U42(tt, U21(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(U21(U31(z0, z1)))) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, U21(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(U21(plus(z0, z1)))) A__U42(tt, U21(tt), x1) -> c11(A__PLUS(mark(x1), a__U21(tt)), MARK(U21(tt))) A__U42(tt, U21(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U42(tt, U21(0), x1) -> c11(A__PLUS(mark(x1), a__U21(0)), MARK(U21(0))) A__U42(tt, U21(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1))) A__U42(tt, U31(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1))) A__U42(tt, U31(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1))) A__U42(tt, U31(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(U31(U21(z0), x1))) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1))) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1))) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(U31(U42(z0, z1, z2), x1))) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(U31(plus(z0, z1), x1))) A__U42(tt, U31(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(U31(tt, x1))) A__U42(tt, U31(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, z1), x2) -> c11(MARK(U31(x0, z1))) A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), 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U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3))) A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3))) A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0)))) A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U42(tt, x0, 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mark(x0)), MARK(s(U42(z0, z1, z2)))) A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0)))) A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0)) A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0)))) A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0)) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U42(tt, 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c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, z1), x2) -> c11(MARK(U11(x0, z1))) A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U42(tt, U12(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U42(tt, U12(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U42(tt, U12(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(U12(U21(z0)))) A__U42(tt, U12(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, U12(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(U12(plus(z0, z1)))) A__U42(tt, U12(tt), x1) -> c11(A__PLUS(mark(x1), a__U12(tt)), MARK(U12(tt))) A__U42(tt, U12(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U42(tt, U12(0), x1) -> c11(A__PLUS(mark(x1), a__U12(0)), MARK(U12(0))) A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(isNat(plus(z0, z1)))) A__U42(tt, isNat(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(isNat(s(z0)))) A__U42(tt, isNat(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(0), x1) -> c11(MARK(isNat(0))) A__U42(tt, isNat(z0), x1) -> c11(MARK(isNat(z0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(U21(U11(z0, z1)))) A__U42(tt, U21(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(U21(U12(z0)))) A__U42(tt, U21(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U42(tt, U21(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U42(tt, U21(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(U21(U31(z0, z1)))) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, U21(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(U21(plus(z0, z1)))) A__U42(tt, U21(tt), x1) -> c11(A__PLUS(mark(x1), a__U21(tt)), MARK(U21(tt))) A__U42(tt, U21(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U42(tt, U21(0), x1) -> c11(A__PLUS(mark(x1), a__U21(0)), MARK(U21(0))) A__U42(tt, U21(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1))) A__U42(tt, U31(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1))) A__U42(tt, U31(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1))) A__U42(tt, U31(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(U31(U21(z0), x1))) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1))) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1))) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(U31(U42(z0, z1, z2), x1))) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(U31(plus(z0, z1), x1))) A__U42(tt, U31(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(U31(tt, x1))) A__U42(tt, U31(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, z1), x2) -> c11(MARK(U31(x0, z1))) A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (195) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) by A__U42(tt, U41(x0, z1, z2), x3) -> c11(A__PLUS(mark(x3), U41(mark(x0), z1, z2)), MARK(U41(x0, z1, z2))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2))) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2))) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2))) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(U41(U21(z0), x1, x2))) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2))) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2))) A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(U41(0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) ---------------------------------------- (196) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), 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A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, z1), x2) -> c11(MARK(U31(x0, z1))) A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1))) A__U42(tt, U41(x0, z1, z2), x3) -> c11(A__PLUS(mark(x3), U41(mark(x0), z1, z2)), MARK(U41(x0, z1, z2))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2))) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2))) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2))) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(U41(U21(z0), x1, x2))) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2))) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2))) A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(U41(0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), 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a__U21(0)), MARK(U21(0))) A__U42(tt, U21(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1))) A__U42(tt, U31(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1))) A__U42(tt, U31(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1))) A__U42(tt, U31(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(U31(U21(z0), x1))) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1))) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1))) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(U31(U42(z0, z1, z2), x1))) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(U31(plus(z0, z1), x1))) A__U42(tt, U31(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(U31(tt, x1))) A__U42(tt, U31(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, z1), x2) -> c11(MARK(U31(x0, z1))) A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1))) A__U42(tt, U41(x0, z1, z2), x3) -> c11(A__PLUS(mark(x3), U41(mark(x0), z1, z2)), MARK(U41(x0, z1, z2))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2))) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2))) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2))) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(U41(U21(z0), x1, x2))) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2))) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2))) A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(U41(0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (197) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (198) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), 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mark(x0)), MARK(U31(x1, z1))) A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2))) A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2))) A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2))) A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2))) A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2))) A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0))) A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3))) A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3))) A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3))) A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3))) A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2))) A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3))) A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3))) A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3))) A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3))) A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3))) A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0)))) A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2)))) A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2))) A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2))) A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2))) A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2))) A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0)))) A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0)))) A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1)))) A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2)))) A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2)))) A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0)))) A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0)) A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0)))) A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0)) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1))) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1))) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, z1), x2) -> c11(MARK(U11(x0, z1))) A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U42(tt, U12(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U42(tt, U12(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U42(tt, U12(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(U12(U21(z0)))) A__U42(tt, U12(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, U12(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(U12(plus(z0, z1)))) A__U42(tt, U12(tt), x1) -> c11(A__PLUS(mark(x1), a__U12(tt)), MARK(U12(tt))) A__U42(tt, U12(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U42(tt, U12(0), x1) -> c11(A__PLUS(mark(x1), a__U12(0)), MARK(U12(0))) A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(isNat(plus(z0, z1)))) A__U42(tt, isNat(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(isNat(s(z0)))) A__U42(tt, isNat(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(0), x1) -> c11(MARK(isNat(0))) A__U42(tt, isNat(z0), x1) -> c11(MARK(isNat(z0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(U21(U11(z0, z1)))) A__U42(tt, U21(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(U21(U12(z0)))) A__U42(tt, U21(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U42(tt, U21(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U42(tt, U21(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(U21(U31(z0, z1)))) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, U21(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(U21(plus(z0, z1)))) A__U42(tt, U21(tt), x1) -> c11(A__PLUS(mark(x1), a__U21(tt)), MARK(U21(tt))) A__U42(tt, U21(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U42(tt, U21(0), x1) -> c11(A__PLUS(mark(x1), a__U21(0)), MARK(U21(0))) A__U42(tt, U21(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1))) A__U42(tt, U31(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1))) A__U42(tt, U31(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1))) A__U42(tt, U31(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(U31(U21(z0), x1))) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1))) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1))) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(U31(U42(z0, z1, z2), x1))) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(U31(plus(z0, z1), x1))) A__U42(tt, U31(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(U31(tt, x1))) A__U42(tt, U31(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, z1), x2) -> c11(MARK(U31(x0, z1))) A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2))) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2))) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2))) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(U41(U21(z0), x1, x2))) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2))) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2))) A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, z1, z2), x3) -> c11(MARK(U41(x0, z1, z2))) A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), 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x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, z1), x2) -> c11(MARK(U11(x0, z1))) A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U42(tt, U12(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U42(tt, U12(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U42(tt, U12(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(U12(U21(z0)))) A__U42(tt, U12(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, U12(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(U12(plus(z0, z1)))) A__U42(tt, U12(tt), x1) -> c11(A__PLUS(mark(x1), a__U12(tt)), MARK(U12(tt))) A__U42(tt, U12(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U42(tt, U12(0), x1) -> c11(A__PLUS(mark(x1), a__U12(0)), MARK(U12(0))) A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(isNat(plus(z0, z1)))) A__U42(tt, isNat(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(isNat(s(z0)))) A__U42(tt, isNat(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(0), x1) -> c11(MARK(isNat(0))) A__U42(tt, isNat(z0), x1) -> c11(MARK(isNat(z0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(U21(U11(z0, z1)))) A__U42(tt, U21(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(U21(U12(z0)))) A__U42(tt, U21(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U42(tt, U21(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U42(tt, U21(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(U21(U31(z0, z1)))) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, U21(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(U21(plus(z0, z1)))) A__U42(tt, U21(tt), x1) -> c11(A__PLUS(mark(x1), a__U21(tt)), MARK(U21(tt))) A__U42(tt, U21(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U42(tt, U21(0), x1) -> c11(A__PLUS(mark(x1), a__U21(0)), MARK(U21(0))) A__U42(tt, U21(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1))) A__U42(tt, U31(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1))) A__U42(tt, U31(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1))) A__U42(tt, U31(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(U31(U21(z0), x1))) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1))) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1))) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(U31(U42(z0, z1, z2), x1))) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(U31(plus(z0, z1), x1))) A__U42(tt, U31(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(U31(tt, x1))) A__U42(tt, U31(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, z1), x2) -> c11(MARK(U31(x0, z1))) A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2))) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2))) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2))) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(U41(U21(z0), x1, x2))) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2))) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2))) A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, z1, z2), x3) -> c11(MARK(U41(x0, z1, z2))) A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (199) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) by A__U42(tt, U42(x0, z1, z2), x3) -> c11(A__PLUS(mark(x3), U42(mark(x0), z1, z2)), MARK(U42(x0, z1, z2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(U42(U11(z0, z1), x1, x2))) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(U42(U12(z0), x1, x2))) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(U42(isNat(z0), x1, x2))) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(U42(U21(z0), x1, x2))) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(U42(U31(z0, z1), x1, x2))) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U42(U41(z0, z1, z2), x1, x2))) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U42(U42(z0, z1, z2), x1, x2))) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U42(plus(z0, z1), x1, x2))) A__U42(tt, U42(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(U42(tt, x1, x2))) A__U42(tt, U42(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(U42(s(z0), x1, x2))) A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(U42(0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) ---------------------------------------- (200) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, 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a__U21(a__U31(mark(z0), z1))), MARK(U21(U31(z0, z1)))) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, U21(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(U21(plus(z0, z1)))) A__U42(tt, U21(tt), x1) -> c11(A__PLUS(mark(x1), a__U21(tt)), MARK(U21(tt))) A__U42(tt, U21(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U42(tt, U21(0), x1) -> c11(A__PLUS(mark(x1), a__U21(0)), MARK(U21(0))) A__U42(tt, U21(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1))) A__U42(tt, U31(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1))) A__U42(tt, U31(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1))) A__U42(tt, U31(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(U31(U21(z0), x1))) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1))) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1))) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(U31(U42(z0, z1, z2), x1))) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(U31(plus(z0, z1), x1))) A__U42(tt, U31(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(U31(tt, x1))) A__U42(tt, U31(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, z1), x2) -> c11(MARK(U31(x0, z1))) A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2))) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2))) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2))) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(U41(U21(z0), x1, x2))) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2))) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2))) A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, z1, z2), x3) -> c11(MARK(U41(x0, z1, z2))) A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2))) A__U42(tt, U42(x0, z1, z2), x3) -> c11(A__PLUS(mark(x3), U42(mark(x0), z1, z2)), MARK(U42(x0, z1, z2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(U42(U11(z0, z1), x1, x2))) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(U42(U12(z0), x1, x2))) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(U42(isNat(z0), x1, x2))) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(U42(U21(z0), x1, x2))) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(U42(U31(z0, z1), x1, x2))) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U42(U41(z0, z1, z2), x1, x2))) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U42(U42(z0, z1, z2), x1, x2))) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U42(plus(z0, z1), x1, x2))) A__U42(tt, U42(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(U42(tt, x1, x2))) A__U42(tt, U42(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(U42(s(z0), x1, x2))) A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(U42(0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) 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x1))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, z1), x2) -> c11(MARK(U31(x0, z1))) A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2))) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2))) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2))) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(U41(U21(z0), x1, x2))) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2))) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2))) A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, z1, z2), x3) -> c11(MARK(U41(x0, z1, z2))) A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2))) A__U42(tt, U42(x0, z1, z2), x3) -> c11(A__PLUS(mark(x3), U42(mark(x0), z1, z2)), MARK(U42(x0, z1, z2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(U42(U11(z0, z1), x1, x2))) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(U42(U12(z0), x1, x2))) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(U42(isNat(z0), x1, x2))) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(U42(U21(z0), x1, x2))) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(U42(U31(z0, z1), x1, x2))) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U42(U41(z0, z1, z2), x1, x2))) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U42(U42(z0, z1, z2), x1, x2))) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U42(plus(z0, z1), x1, x2))) A__U42(tt, U42(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(U42(tt, x1, x2))) A__U42(tt, U42(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(U42(s(z0), x1, x2))) A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(U42(0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (201) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (202) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> 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a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(isNat(plus(z0, z1)))) A__U42(tt, isNat(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(isNat(s(z0)))) A__U42(tt, isNat(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(0), x1) -> c11(MARK(isNat(0))) A__U42(tt, isNat(z0), x1) -> c11(MARK(isNat(z0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(U21(U11(z0, z1)))) A__U42(tt, U21(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(U21(U12(z0)))) A__U42(tt, U21(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U42(tt, U21(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U42(tt, U21(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(U21(U31(z0, z1)))) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, U21(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(U21(plus(z0, z1)))) A__U42(tt, U21(tt), x1) -> c11(A__PLUS(mark(x1), a__U21(tt)), MARK(U21(tt))) A__U42(tt, U21(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U42(tt, U21(0), x1) -> c11(A__PLUS(mark(x1), a__U21(0)), MARK(U21(0))) A__U42(tt, U21(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1))) A__U42(tt, U31(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1))) A__U42(tt, U31(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1))) A__U42(tt, U31(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(U31(U21(z0), x1))) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1))) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1))) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(U31(U42(z0, z1, z2), x1))) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(U31(plus(z0, z1), x1))) A__U42(tt, U31(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(U31(tt, x1))) A__U42(tt, U31(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, z1), x2) -> c11(MARK(U31(x0, z1))) A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2))) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2))) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2))) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(U41(U21(z0), x1, x2))) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2))) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2))) A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, z1, z2), x3) -> c11(MARK(U41(x0, z1, z2))) A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(U42(U11(z0, z1), x1, x2))) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(U42(U12(z0), x1, x2))) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(U42(isNat(z0), x1, x2))) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(U42(U21(z0), x1, x2))) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(U42(U31(z0, z1), x1, x2))) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U42(U41(z0, z1, z2), x1, x2))) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U42(U42(z0, z1, z2), x1, x2))) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U42(plus(z0, z1), x1, x2))) A__U42(tt, U42(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(U42(tt, x1, x2))) A__U42(tt, U42(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(U42(s(z0), x1, x2))) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, z1, z2), x3) -> c11(MARK(U42(x0, z1, z2))) A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, 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A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> 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A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2))) A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U42(tt, x0, 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c11(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1))) A__U42(tt, U31(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1))) A__U42(tt, U31(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1))) A__U42(tt, U31(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(U31(U21(z0), x1))) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1))) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1))) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(U31(U42(z0, z1, z2), x1))) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(U31(plus(z0, z1), x1))) A__U42(tt, U31(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(U31(tt, x1))) A__U42(tt, U31(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, z1), x2) -> c11(MARK(U31(x0, z1))) A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2))) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2))) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2))) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(U41(U21(z0), x1, x2))) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2))) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2))) A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, z1, z2), x3) -> c11(MARK(U41(x0, z1, z2))) A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(U42(U11(z0, z1), x1, x2))) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(U42(U12(z0), x1, x2))) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(U42(isNat(z0), x1, x2))) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(U42(U21(z0), x1, x2))) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(U42(U31(z0, z1), x1, x2))) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U42(U41(z0, z1, z2), x1, x2))) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U42(U42(z0, z1, z2), x1, x2))) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U42(plus(z0, z1), x1, x2))) A__U42(tt, U42(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(U42(tt, x1, x2))) A__U42(tt, U42(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(U42(s(z0), x1, x2))) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, z1, z2), x3) -> c11(MARK(U42(x0, z1, z2))) A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (203) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) by A__U42(tt, plus(x0, x1), x2) -> c11(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U42(tt, plus(x0, U12(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(plus(x0, U12(z0)))) A__U42(tt, plus(x0, isNat(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U42(tt, plus(x0, U21(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(plus(x0, U21(z0)))) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(plus(x0, U31(z0, z1)))) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(plus(x0, U41(z0, z1, z2)))) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(plus(x0, U42(z0, z1, z2)))) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U42(tt, plus(x0, tt), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U42(tt, plus(x0, s(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U42(tt, plus(x0, 0), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U42(tt, plus(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(plus(U12(z0), x1))) A__U42(tt, plus(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U42(tt, plus(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(plus(U21(z0), x1))) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(plus(U31(z0, z1), x1))) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1))) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(plus(U42(z0, z1, z2), x1))) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) ---------------------------------------- (204) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, 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A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2))) A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, 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A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, z1), x2) -> c11(MARK(U31(x0, z1))) A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2))) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2))) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2))) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(U41(U21(z0), x1, x2))) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2))) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2))) A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, z1, z2), x3) -> c11(MARK(U41(x0, z1, z2))) A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(U42(U11(z0, z1), x1, x2))) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(U42(U12(z0), x1, x2))) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(U42(isNat(z0), x1, x2))) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(U42(U21(z0), x1, x2))) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(U42(U31(z0, z1), x1, x2))) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U42(U41(z0, z1, z2), x1, x2))) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U42(U42(z0, z1, z2), x1, x2))) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U42(plus(z0, z1), x1, x2))) A__U42(tt, U42(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(U42(tt, x1, x2))) A__U42(tt, U42(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(U42(s(z0), x1, x2))) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, z1, z2), x3) -> c11(MARK(U42(x0, z1, z2))) A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2))) A__U42(tt, plus(x0, x1), x2) -> c11(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U42(tt, plus(x0, U12(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(plus(x0, U12(z0)))) A__U42(tt, plus(x0, isNat(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U42(tt, plus(x0, U21(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(plus(x0, U21(z0)))) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(plus(x0, U31(z0, z1)))) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(plus(x0, U41(z0, z1, z2)))) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(plus(x0, U42(z0, z1, z2)))) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U42(tt, plus(x0, tt), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U42(tt, plus(x0, s(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U42(tt, plus(x0, 0), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U42(tt, plus(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(plus(U12(z0), x1))) A__U42(tt, plus(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U42(tt, plus(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(plus(U21(z0), x1))) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(plus(U31(z0, z1), x1))) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1))) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(plus(U42(z0, z1, z2), x1))) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> 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0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2))) A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2))) A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2))) A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2))) A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2))) A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0))) A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3))) A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3))) A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3))) A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3))) A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2))) A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3))) A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3))) A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3))) A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3))) A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3))) A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0)))) A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2)))) A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2))) A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2))) A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2))) A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2))) A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0)))) A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0)))) A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1)))) A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2)))) A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), 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A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, z1), x2) -> c11(MARK(U31(x0, z1))) A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2))) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2))) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2))) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(U41(U21(z0), x1, x2))) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2))) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2))) A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, z1, z2), x3) -> c11(MARK(U41(x0, z1, z2))) A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(U42(U11(z0, z1), x1, x2))) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(U42(U12(z0), x1, x2))) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(U42(isNat(z0), x1, x2))) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(U42(U21(z0), x1, x2))) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(U42(U31(z0, z1), x1, x2))) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U42(U41(z0, z1, z2), x1, x2))) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U42(U42(z0, z1, z2), x1, x2))) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U42(plus(z0, z1), x1, x2))) A__U42(tt, U42(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(U42(tt, x1, x2))) A__U42(tt, U42(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(U42(s(z0), x1, x2))) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, z1, z2), x3) -> c11(MARK(U42(x0, z1, z2))) A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2))) A__U42(tt, plus(x0, x1), x2) -> c11(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U42(tt, plus(x0, U12(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(plus(x0, U12(z0)))) A__U42(tt, plus(x0, isNat(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U42(tt, plus(x0, U21(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(plus(x0, U21(z0)))) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(plus(x0, U31(z0, z1)))) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(plus(x0, U41(z0, z1, z2)))) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(plus(x0, U42(z0, z1, z2)))) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U42(tt, plus(x0, tt), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U42(tt, plus(x0, s(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U42(tt, plus(x0, 0), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U42(tt, plus(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(plus(U12(z0), x1))) A__U42(tt, plus(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U42(tt, plus(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(plus(U21(z0), x1))) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(plus(U31(z0, z1), x1))) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1))) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(plus(U42(z0, z1, z2), x1))) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (205) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (206) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2)) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2)) A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2))) A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2))) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0))) A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1))) A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1))) A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1))) A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1)))) A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0)))) A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0)))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1))) A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1))) A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1))) A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1))) A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1)))) A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0)))) A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0)))) A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0)))) A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1)))) A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), 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a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2))) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2))) A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, z1, z2), x3) -> c11(MARK(U41(x0, z1, z2))) A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(U42(U11(z0, z1), x1, x2))) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(U42(U12(z0), x1, x2))) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(U42(isNat(z0), x1, x2))) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(U42(U21(z0), x1, x2))) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(U42(U31(z0, z1), x1, x2))) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U42(U41(z0, z1, z2), x1, x2))) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U42(U42(z0, z1, z2), x1, x2))) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U42(plus(z0, z1), x1, x2))) A__U42(tt, U42(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(U42(tt, x1, x2))) A__U42(tt, U42(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(U42(s(z0), x1, x2))) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, z1, z2), x3) -> c11(MARK(U42(x0, z1, z2))) A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U42(tt, plus(x0, U12(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(plus(x0, U12(z0)))) A__U42(tt, plus(x0, isNat(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U42(tt, plus(x0, U21(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(plus(x0, U21(z0)))) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(plus(x0, U31(z0, z1)))) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(plus(x0, U41(z0, z1, z2)))) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(plus(x0, U42(z0, z1, z2)))) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U42(tt, plus(x0, tt), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U42(tt, plus(x0, s(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U42(tt, plus(x0, 0), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U42(tt, plus(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(plus(U12(z0), x1))) A__U42(tt, plus(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U42(tt, plus(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(plus(U21(z0), x1))) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(plus(U31(z0, z1), x1))) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1))) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(plus(U42(z0, z1, z2), x1))) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), x2) -> c11(MARK(plus(x0, x1))) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, 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c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(isNat(plus(z0, z1)))) A__U42(tt, isNat(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(isNat(s(z0)))) A__U42(tt, isNat(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(0), x1) -> c11(MARK(isNat(0))) A__U42(tt, isNat(z0), x1) -> c11(MARK(isNat(z0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(U21(U11(z0, z1)))) A__U42(tt, U21(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(U21(U12(z0)))) A__U42(tt, U21(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U42(tt, U21(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U42(tt, U21(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(U21(U31(z0, z1)))) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, U21(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(U21(plus(z0, z1)))) A__U42(tt, U21(tt), x1) -> c11(A__PLUS(mark(x1), a__U21(tt)), MARK(U21(tt))) A__U42(tt, U21(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U42(tt, U21(0), x1) -> c11(A__PLUS(mark(x1), a__U21(0)), MARK(U21(0))) A__U42(tt, U21(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1))) A__U42(tt, U31(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1))) A__U42(tt, U31(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1))) A__U42(tt, U31(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(U31(U21(z0), x1))) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1))) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1))) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(U31(U42(z0, z1, z2), x1))) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(U31(plus(z0, z1), x1))) A__U42(tt, U31(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(U31(tt, x1))) A__U42(tt, U31(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, z1), x2) -> c11(MARK(U31(x0, z1))) A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2))) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2))) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2))) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(U41(U21(z0), x1, x2))) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2))) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2))) A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, z1, z2), x3) -> c11(MARK(U41(x0, z1, z2))) A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(U42(U11(z0, z1), x1, x2))) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(U42(U12(z0), x1, x2))) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(U42(isNat(z0), x1, x2))) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(U42(U21(z0), x1, x2))) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(U42(U31(z0, z1), x1, x2))) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U42(U41(z0, z1, z2), x1, x2))) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U42(U42(z0, z1, z2), x1, x2))) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U42(plus(z0, z1), x1, x2))) A__U42(tt, U42(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(U42(tt, x1, x2))) A__U42(tt, U42(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(U42(s(z0), x1, x2))) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, z1, z2), x3) -> c11(MARK(U42(x0, z1, z2))) A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U42(tt, plus(x0, U12(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(plus(x0, U12(z0)))) A__U42(tt, plus(x0, isNat(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U42(tt, plus(x0, U21(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(plus(x0, U21(z0)))) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(plus(x0, U31(z0, z1)))) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(plus(x0, U41(z0, z1, z2)))) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(plus(x0, U42(z0, z1, z2)))) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U42(tt, plus(x0, tt), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U42(tt, plus(x0, s(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U42(tt, plus(x0, 0), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U42(tt, plus(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(plus(U12(z0), x1))) A__U42(tt, plus(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U42(tt, plus(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(plus(U21(z0), x1))) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(plus(U31(z0, z1), x1))) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1))) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(plus(U42(z0, z1, z2), x1))) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), x2) -> c11(MARK(plus(x0, x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (207) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) by A__U42(tt, U11(z0, z1), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, tt, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), tt), MARK(tt)) A__U42(tt, s(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U42(tt, 0, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), 0), MARK(0)) A__U42(tt, x0, U11(x1, z1)) -> c11(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U12(z0), x2)) -> c11(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(isNat(z0), x2)) -> c11(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U21(z0), x2)) -> c11(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(tt, x2)) -> c11(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(s(z0), x2)) -> c11(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(0, x2)) -> c11(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) ---------------------------------------- (208) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> 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0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2))) A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2))) A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2))) A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2))) A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2))) A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0))) A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3))) A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3))) A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3))) A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3))) A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2))) A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3))) A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3))) A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3))) A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3))) A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3))) A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0)))) A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2)))) A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2))) A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2))) A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2))) A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2))) A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0)))) A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0)))) A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1)))) A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2)))) A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), 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A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, z1), x2) -> c11(MARK(U31(x0, z1))) A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2))) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2))) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, 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-> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, z1, z2), x3) -> c11(MARK(U41(x0, z1, z2))) A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(U42(U11(z0, z1), x1, x2))) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(U42(U12(z0), x1, x2))) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(U42(isNat(z0), x1, x2))) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(U42(U21(z0), x1, x2))) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(U42(U31(z0, z1), x1, x2))) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U42(U41(z0, z1, z2), x1, x2))) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U42(U42(z0, z1, z2), x1, x2))) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U42(plus(z0, z1), x1, x2))) A__U42(tt, U42(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(U42(tt, x1, x2))) A__U42(tt, U42(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(U42(s(z0), x1, x2))) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, z1, z2), x3) -> c11(MARK(U42(x0, z1, z2))) A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U42(tt, plus(x0, U12(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(plus(x0, U12(z0)))) A__U42(tt, plus(x0, isNat(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U42(tt, plus(x0, U21(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(plus(x0, U21(z0)))) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(plus(x0, U31(z0, z1)))) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(plus(x0, U41(z0, z1, z2)))) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(plus(x0, U42(z0, z1, z2)))) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U42(tt, plus(x0, tt), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U42(tt, plus(x0, s(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U42(tt, plus(x0, 0), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U42(tt, plus(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(plus(U12(z0), x1))) A__U42(tt, plus(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U42(tt, plus(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(plus(U21(z0), x1))) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(plus(U31(z0, z1), x1))) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1))) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(plus(U42(z0, z1, z2), x1))) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), x2) -> c11(MARK(plus(x0, x1))) A__U42(tt, tt, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), tt), MARK(tt)) A__U42(tt, s(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U42(tt, 0, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), 0), MARK(0)) A__U42(tt, x0, U11(x1, z1)) -> c11(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U12(z0), x2)) -> c11(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(isNat(z0), x2)) -> c11(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U21(z0), x2)) -> c11(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(tt, x2)) -> c11(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(s(z0), x2)) -> c11(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(0, x2)) -> c11(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) 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a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, z1), x2) -> c11(MARK(U31(x0, z1))) A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2))) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2))) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2))) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(U41(U21(z0), x1, x2))) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2))) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2))) A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, z1, z2), x3) -> c11(MARK(U41(x0, z1, z2))) A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(U42(U11(z0, z1), x1, x2))) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(U42(U12(z0), x1, x2))) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(U42(isNat(z0), x1, x2))) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(U42(U21(z0), x1, x2))) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(U42(U31(z0, z1), x1, x2))) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U42(U41(z0, z1, z2), x1, x2))) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U42(U42(z0, z1, z2), x1, x2))) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U42(plus(z0, z1), x1, x2))) A__U42(tt, U42(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(U42(tt, x1, x2))) A__U42(tt, U42(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(U42(s(z0), x1, x2))) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, z1, z2), x3) -> c11(MARK(U42(x0, z1, z2))) A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U42(tt, plus(x0, U12(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(plus(x0, U12(z0)))) A__U42(tt, plus(x0, isNat(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U42(tt, plus(x0, U21(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(plus(x0, U21(z0)))) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(plus(x0, U31(z0, z1)))) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(plus(x0, U41(z0, z1, z2)))) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(plus(x0, U42(z0, z1, z2)))) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U42(tt, plus(x0, tt), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U42(tt, plus(x0, s(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U42(tt, plus(x0, 0), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U42(tt, plus(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(plus(U12(z0), x1))) A__U42(tt, plus(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U42(tt, plus(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(plus(U21(z0), x1))) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(plus(U31(z0, z1), x1))) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1))) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(plus(U42(z0, z1, z2), x1))) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), x2) -> c11(MARK(plus(x0, x1))) A__U42(tt, tt, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), tt), MARK(tt)) A__U42(tt, s(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U42(tt, 0, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), 0), MARK(0)) A__U42(tt, x0, U11(x1, z1)) -> c11(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U12(z0), x2)) -> c11(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(isNat(z0), x2)) -> c11(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U21(z0), x2)) -> c11(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(tt, x2)) -> c11(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(s(z0), x2)) -> c11(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(0, x2)) -> c11(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (209) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U42(tt, tt, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), tt), MARK(tt)) ---------------------------------------- (210) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, 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x2)), MARK(U41(isNat(z0), x1, x2))) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(U41(U21(z0), x1, x2))) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2))) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2))) A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, z1, z2), x3) -> c11(MARK(U41(x0, z1, z2))) A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(U42(U11(z0, z1), x1, x2))) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(U42(U12(z0), x1, x2))) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(U42(isNat(z0), x1, x2))) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(U42(U21(z0), x1, x2))) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(U42(U31(z0, z1), x1, x2))) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U42(U41(z0, z1, z2), x1, x2))) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U42(U42(z0, z1, z2), x1, x2))) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U42(plus(z0, z1), x1, x2))) A__U42(tt, U42(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(U42(tt, x1, x2))) A__U42(tt, U42(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(U42(s(z0), x1, x2))) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, z1, z2), x3) -> c11(MARK(U42(x0, z1, z2))) A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U42(tt, plus(x0, U12(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(plus(x0, U12(z0)))) A__U42(tt, plus(x0, isNat(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U42(tt, plus(x0, U21(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(plus(x0, U21(z0)))) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(plus(x0, U31(z0, z1)))) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(plus(x0, U41(z0, z1, z2)))) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(plus(x0, U42(z0, z1, z2)))) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U42(tt, plus(x0, tt), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U42(tt, plus(x0, s(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U42(tt, plus(x0, 0), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U42(tt, plus(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(plus(U12(z0), x1))) A__U42(tt, plus(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U42(tt, plus(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(plus(U21(z0), x1))) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(plus(U31(z0, z1), x1))) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1))) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(plus(U42(z0, z1, z2), x1))) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), x2) -> c11(MARK(plus(x0, x1))) A__U42(tt, s(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U42(tt, 0, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), 0), MARK(0)) A__U42(tt, x0, U11(x1, z1)) -> c11(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U12(z0), x2)) -> c11(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(isNat(z0), x2)) -> c11(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U21(z0), x2)) -> c11(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(tt, x2)) -> c11(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(s(z0), x2)) -> c11(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(0, x2)) -> c11(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, 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0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2))) A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2))) A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2))) A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2))) A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2))) A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0))) A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3))) A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3))) A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3))) A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3))) A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2))) A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3))) A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3))) A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3))) A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3))) A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3))) A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0)))) A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2)))) A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2))) A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2))) A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2))) A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2))) A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0)))) A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0)))) A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1)))) A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2)))) A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), 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A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, z1), x2) -> c11(MARK(U31(x0, z1))) A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2))) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2))) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2))) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(U41(U21(z0), x1, x2))) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2))) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2))) A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, z1, z2), x3) -> c11(MARK(U41(x0, z1, z2))) A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(U42(U11(z0, z1), x1, x2))) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(U42(U12(z0), x1, x2))) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(U42(isNat(z0), x1, x2))) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(U42(U21(z0), x1, x2))) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(U42(U31(z0, z1), x1, x2))) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U42(U41(z0, z1, z2), x1, x2))) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U42(U42(z0, z1, z2), x1, x2))) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U42(plus(z0, z1), x1, x2))) A__U42(tt, U42(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(U42(tt, x1, x2))) A__U42(tt, U42(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(U42(s(z0), x1, x2))) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, z1, z2), x3) -> c11(MARK(U42(x0, z1, z2))) A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U42(tt, plus(x0, U12(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(plus(x0, U12(z0)))) A__U42(tt, plus(x0, isNat(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U42(tt, plus(x0, U21(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(plus(x0, U21(z0)))) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(plus(x0, U31(z0, z1)))) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(plus(x0, U41(z0, z1, z2)))) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(plus(x0, U42(z0, z1, z2)))) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U42(tt, plus(x0, tt), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U42(tt, plus(x0, s(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U42(tt, plus(x0, 0), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U42(tt, plus(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(plus(U12(z0), x1))) A__U42(tt, plus(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U42(tt, plus(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(plus(U21(z0), x1))) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(plus(U31(z0, z1), x1))) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1))) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(plus(U42(z0, z1, z2), x1))) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), x2) -> c11(MARK(plus(x0, x1))) A__U42(tt, s(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U42(tt, 0, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), 0), MARK(0)) A__U42(tt, x0, U11(x1, z1)) -> c11(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U12(z0), x2)) -> c11(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(isNat(z0), x2)) -> c11(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U21(z0), x2)) -> c11(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(tt, x2)) -> c11(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(s(z0), x2)) -> c11(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(0, x2)) -> c11(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (211) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (212) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3)) A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3)) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> 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A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2))) A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0))) A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3))) A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3))) A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3))) A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3))) A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2))) A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3))) A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3))) A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3))) A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3))) A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3))) A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0)))) A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2)))) A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2))) A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2))) A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2))) A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2))) A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0)))) A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0)))) A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1)))) A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2)))) A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2)))) A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0)))) A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0)) A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0)))) A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0)) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1))) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1))) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, z1), x2) -> c11(MARK(U11(x0, z1))) A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U42(tt, U12(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U42(tt, U12(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U42(tt, U12(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(U12(U21(z0)))) A__U42(tt, U12(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, U12(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(U12(plus(z0, z1)))) A__U42(tt, U12(tt), x1) -> c11(A__PLUS(mark(x1), a__U12(tt)), MARK(U12(tt))) A__U42(tt, U12(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U42(tt, U12(0), x1) -> c11(A__PLUS(mark(x1), a__U12(0)), MARK(U12(0))) A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(isNat(plus(z0, z1)))) A__U42(tt, isNat(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(isNat(s(z0)))) A__U42(tt, isNat(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(0), x1) -> c11(MARK(isNat(0))) A__U42(tt, isNat(z0), x1) -> c11(MARK(isNat(z0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(U21(U11(z0, z1)))) A__U42(tt, U21(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(U21(U12(z0)))) A__U42(tt, U21(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U42(tt, U21(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U42(tt, U21(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(U21(U31(z0, z1)))) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, U21(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(U21(plus(z0, z1)))) A__U42(tt, U21(tt), x1) -> c11(A__PLUS(mark(x1), a__U21(tt)), MARK(U21(tt))) A__U42(tt, U21(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U42(tt, U21(0), x1) -> c11(A__PLUS(mark(x1), a__U21(0)), MARK(U21(0))) A__U42(tt, U21(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1))) A__U42(tt, U31(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1))) A__U42(tt, U31(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1))) A__U42(tt, U31(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(U31(U21(z0), x1))) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1))) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1))) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(U31(U42(z0, z1, z2), x1))) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(U31(plus(z0, z1), x1))) A__U42(tt, U31(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(U31(tt, x1))) A__U42(tt, U31(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, z1), x2) -> c11(MARK(U31(x0, z1))) A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2))) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2))) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2))) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(U41(U21(z0), x1, x2))) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2))) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2))) A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, z1, z2), x3) -> c11(MARK(U41(x0, z1, z2))) A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(U42(U11(z0, z1), x1, x2))) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(U42(U12(z0), x1, x2))) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(U42(isNat(z0), x1, x2))) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(U42(U21(z0), x1, x2))) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(U42(U31(z0, z1), x1, x2))) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U42(U41(z0, z1, z2), x1, x2))) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U42(U42(z0, z1, z2), x1, x2))) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U42(plus(z0, z1), x1, x2))) A__U42(tt, U42(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(U42(tt, x1, x2))) A__U42(tt, U42(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(U42(s(z0), x1, x2))) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, z1, z2), x3) -> c11(MARK(U42(x0, z1, z2))) A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U42(tt, plus(x0, U12(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(plus(x0, U12(z0)))) A__U42(tt, plus(x0, isNat(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U42(tt, plus(x0, U21(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(plus(x0, U21(z0)))) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(plus(x0, U31(z0, z1)))) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(plus(x0, U41(z0, z1, z2)))) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(plus(x0, U42(z0, z1, z2)))) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U42(tt, plus(x0, tt), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U42(tt, plus(x0, s(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U42(tt, plus(x0, 0), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U42(tt, plus(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(plus(U12(z0), x1))) A__U42(tt, plus(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U42(tt, plus(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(plus(U21(z0), x1))) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(plus(U31(z0, z1), x1))) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1))) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(plus(U42(z0, z1, z2), x1))) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), x2) -> c11(MARK(plus(x0, x1))) A__U42(tt, s(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(x1, z1)) -> c11(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U12(z0), x2)) -> c11(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(isNat(z0), x2)) -> c11(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U21(z0), x2)) -> c11(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(tt, x2)) -> c11(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(s(z0), x2)) -> c11(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(0, x2)) -> c11(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U42(tt, 0, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), 0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) 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-> c10(MARK(x3)) A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3)) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3)) A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3)) A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3)) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0))) A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3)) A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2)) A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U42(tt, 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x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2)) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), 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U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2))) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2))) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2))) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2))) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0))) A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1))) A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1))) A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1))) A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1)))) A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0)))) A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) 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x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, z1), x2) -> c11(MARK(U31(x0, z1))) A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2))) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2))) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2))) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(U41(U21(z0), x1, x2))) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2))) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2))) A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, z1, z2), x3) -> c11(MARK(U41(x0, z1, z2))) A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(U42(U11(z0, z1), x1, x2))) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(U42(U12(z0), x1, x2))) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(U42(isNat(z0), x1, x2))) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(U42(U21(z0), x1, x2))) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(U42(U31(z0, z1), x1, x2))) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U42(U41(z0, z1, z2), x1, x2))) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U42(U42(z0, z1, z2), x1, x2))) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U42(plus(z0, z1), x1, x2))) A__U42(tt, U42(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(U42(tt, x1, x2))) A__U42(tt, U42(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(U42(s(z0), x1, x2))) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, z1, z2), x3) -> c11(MARK(U42(x0, z1, z2))) A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U42(tt, plus(x0, U12(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(plus(x0, U12(z0)))) A__U42(tt, plus(x0, isNat(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U42(tt, plus(x0, U21(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(plus(x0, U21(z0)))) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(plus(x0, U31(z0, z1)))) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(plus(x0, U41(z0, z1, z2)))) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(plus(x0, U42(z0, z1, z2)))) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U42(tt, plus(x0, tt), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U42(tt, plus(x0, s(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U42(tt, plus(x0, 0), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U42(tt, plus(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(plus(U12(z0), x1))) A__U42(tt, plus(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U42(tt, plus(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(plus(U21(z0), x1))) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(plus(U31(z0, z1), x1))) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1))) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(plus(U42(z0, z1, z2), x1))) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), x2) -> c11(MARK(plus(x0, x1))) A__U42(tt, s(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(x1, z1)) -> c11(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U12(z0), x2)) -> c11(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(isNat(z0), x2)) -> c11(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U21(z0), x2)) -> c11(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(tt, x2)) -> c11(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(s(z0), x2)) -> c11(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(0, x2)) -> c11(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U42(tt, 0, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), 0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (213) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) by A__U42(tt, U11(z0, z1), U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U42(tt, U12(z0), U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), a__U12(mark(z0))), MARK(U12(z0))) A__U42(tt, isNat(z0), U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), a__isNat(z0)), MARK(isNat(z0))) A__U42(tt, U21(z0), U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), a__U21(mark(z0))), MARK(U21(z0))) A__U42(tt, U31(z0, z1), U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U42(tt, U41(z0, z1, z2), U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U42(tt, U42(z0, z1, z2), U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) A__U42(tt, plus(z0, z1), U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U42(tt, tt, U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), tt), MARK(tt)) A__U42(tt, s(z0), U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U42(tt, 0, U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), 0), MARK(0)) A__U42(tt, x0, U12(x1)) -> c11(A__PLUS(U12(mark(x1)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U11(z0, z1))) -> c11(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U12(z0))) -> c11(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(isNat(z0))) -> c11(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U21(z0))) -> c11(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U31(z0, z1))) -> c11(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c11(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c11(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(plus(z0, z1))) -> c11(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(tt)) -> c11(A__PLUS(a__U12(tt), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(s(z0))) -> c11(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(0)) -> c11(A__PLUS(a__U12(0), mark(x0)), MARK(x0)) ---------------------------------------- (214) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), 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plus(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(plus(U42(z0, z1, z2), x1))) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), x2) -> c11(MARK(plus(x0, x1))) A__U42(tt, s(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(x1, z1)) -> c11(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U12(z0), x2)) -> c11(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(isNat(z0), x2)) -> c11(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U21(z0), x2)) -> c11(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(tt, x2)) -> c11(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(s(z0), x2)) -> c11(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(0, x2)) -> c11(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U42(tt, 0, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), 0)) A__U42(tt, tt, U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), tt), MARK(tt)) A__U42(tt, s(z0), U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U42(tt, 0, U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), 0), MARK(0)) A__U42(tt, x0, U12(x1)) -> c11(A__PLUS(U12(mark(x1)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U11(z0, z1))) -> c11(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U12(z0))) -> c11(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(isNat(z0))) -> c11(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U21(z0))) -> c11(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U31(z0, z1))) -> c11(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c11(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c11(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(plus(z0, z1))) -> c11(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(tt)) -> c11(A__PLUS(a__U12(tt), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(s(z0))) -> c11(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(0)) -> c11(A__PLUS(a__U12(0), mark(x0)), MARK(x0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1))) A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) 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z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), 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z1)), mark(x0)), MARK(U21(U31(z0, z1)))) A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1)))) A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt))) A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0)))) A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0))) A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2))) A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2))) A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2))) A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2))) A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2))) A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0))) A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3))) A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3))) A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3))) A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3))) A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2))) A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3))) A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3))) A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3))) A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3))) A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3))) A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, 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c11(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(U31(tt, x1))) A__U42(tt, U31(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, z1), x2) -> c11(MARK(U31(x0, z1))) A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2))) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2))) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2))) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(U41(U21(z0), x1, x2))) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2))) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2))) A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, z1, z2), x3) -> c11(MARK(U41(x0, z1, z2))) A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(U42(U11(z0, z1), x1, x2))) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(U42(U12(z0), x1, x2))) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(U42(isNat(z0), x1, x2))) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(U42(U21(z0), x1, x2))) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(U42(U31(z0, z1), x1, x2))) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U42(U41(z0, z1, z2), x1, x2))) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U42(U42(z0, z1, z2), x1, x2))) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U42(plus(z0, z1), x1, x2))) A__U42(tt, U42(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(U42(tt, x1, x2))) A__U42(tt, U42(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(U42(s(z0), x1, x2))) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, z1, z2), x3) -> c11(MARK(U42(x0, z1, z2))) A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U42(tt, plus(x0, U12(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(plus(x0, U12(z0)))) A__U42(tt, plus(x0, isNat(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U42(tt, plus(x0, U21(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(plus(x0, U21(z0)))) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(plus(x0, U31(z0, z1)))) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(plus(x0, U41(z0, z1, z2)))) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(plus(x0, U42(z0, z1, z2)))) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U42(tt, plus(x0, tt), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U42(tt, plus(x0, s(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U42(tt, plus(x0, 0), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U42(tt, plus(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(plus(U12(z0), x1))) A__U42(tt, plus(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U42(tt, plus(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(plus(U21(z0), x1))) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(plus(U31(z0, z1), x1))) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1))) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(plus(U42(z0, z1, z2), x1))) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), x2) -> c11(MARK(plus(x0, x1))) A__U42(tt, s(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(x1, z1)) -> c11(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U12(z0), x2)) -> c11(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(isNat(z0), x2)) -> c11(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U21(z0), x2)) -> c11(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(tt, x2)) -> c11(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(s(z0), x2)) -> c11(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(0, x2)) -> c11(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U42(tt, 0, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), 0)) A__U42(tt, tt, U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), tt), MARK(tt)) A__U42(tt, s(z0), U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U42(tt, 0, U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), 0), MARK(0)) A__U42(tt, x0, U12(x1)) -> c11(A__PLUS(U12(mark(x1)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U11(z0, z1))) -> c11(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U12(z0))) -> c11(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(isNat(z0))) -> c11(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U21(z0))) -> c11(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U31(z0, z1))) -> c11(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c11(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c11(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(plus(z0, z1))) -> c11(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(tt)) -> c11(A__PLUS(a__U12(tt), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(s(z0))) -> c11(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(0)) -> c11(A__PLUS(a__U12(0), mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (215) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U42(tt, tt, U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), tt), MARK(tt)) ---------------------------------------- (216) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), 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a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> 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c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), 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c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2))) A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2))) A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2))) A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, 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A__U42(tt, U21(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1))) A__U42(tt, U31(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1))) A__U42(tt, U31(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1))) A__U42(tt, U31(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(U31(U21(z0), x1))) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1))) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1))) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(U31(U42(z0, z1, z2), x1))) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(U31(plus(z0, z1), x1))) A__U42(tt, U31(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(U31(tt, x1))) A__U42(tt, U31(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, z1), x2) -> c11(MARK(U31(x0, z1))) A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2))) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2))) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2))) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(U41(U21(z0), x1, x2))) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2))) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2))) A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, z1, z2), x3) -> c11(MARK(U41(x0, z1, z2))) A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(U42(U11(z0, z1), x1, x2))) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(U42(U12(z0), x1, x2))) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(U42(isNat(z0), x1, x2))) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(U42(U21(z0), x1, x2))) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(U42(U31(z0, z1), x1, x2))) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U42(U41(z0, z1, z2), x1, x2))) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U42(U42(z0, z1, z2), x1, x2))) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U42(plus(z0, z1), x1, x2))) A__U42(tt, U42(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(U42(tt, x1, x2))) A__U42(tt, U42(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(U42(s(z0), x1, x2))) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, z1, z2), x3) -> c11(MARK(U42(x0, z1, z2))) A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U42(tt, plus(x0, U12(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(plus(x0, U12(z0)))) A__U42(tt, plus(x0, isNat(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U42(tt, plus(x0, U21(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(plus(x0, U21(z0)))) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(plus(x0, U31(z0, z1)))) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(plus(x0, U41(z0, z1, z2)))) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(plus(x0, U42(z0, z1, z2)))) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U42(tt, plus(x0, tt), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U42(tt, plus(x0, s(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U42(tt, plus(x0, 0), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U42(tt, plus(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(plus(U12(z0), x1))) A__U42(tt, plus(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U42(tt, plus(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(plus(U21(z0), x1))) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(plus(U31(z0, z1), x1))) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1))) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(plus(U42(z0, z1, z2), x1))) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), x2) -> c11(MARK(plus(x0, x1))) A__U42(tt, s(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(x1, z1)) -> c11(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U12(z0), x2)) -> c11(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(isNat(z0), x2)) -> c11(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U21(z0), x2)) -> c11(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(tt, x2)) -> c11(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(s(z0), x2)) -> c11(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(0, x2)) -> c11(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U42(tt, 0, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), 0)) A__U42(tt, s(z0), U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U42(tt, 0, U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), 0), MARK(0)) A__U42(tt, x0, U12(x1)) -> c11(A__PLUS(U12(mark(x1)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U11(z0, z1))) -> c11(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U12(z0))) -> c11(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(isNat(z0))) -> c11(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U21(z0))) -> c11(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U31(z0, z1))) -> c11(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c11(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c11(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(plus(z0, z1))) -> c11(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(tt)) -> c11(A__PLUS(a__U12(tt), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(s(z0))) -> c11(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(0)) -> c11(A__PLUS(a__U12(0), mark(x0)), MARK(x0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) 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A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0)))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1))) A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1))) A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1))) A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1))) A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1)))) A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0)))) A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0)))) A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0)))) A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1)))) A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1)))) A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt))) A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0)))) A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0))) A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2))) A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2))) A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2))) A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2))) A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2))) A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0))) A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3))) A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3))) A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3))) A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3))) A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2))) A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3))) A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3))) A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3))) A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3))) A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3))) A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), 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plus(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U42(tt, plus(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(plus(U21(z0), x1))) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(plus(U31(z0, z1), x1))) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1))) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(plus(U42(z0, z1, z2), x1))) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), x2) -> c11(MARK(plus(x0, x1))) A__U42(tt, s(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(x1, z1)) -> c11(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U12(z0), x2)) -> c11(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(isNat(z0), x2)) -> c11(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U21(z0), x2)) -> c11(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(tt, x2)) -> c11(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(s(z0), x2)) -> c11(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(0, x2)) -> c11(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U42(tt, 0, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), 0)) A__U42(tt, s(z0), U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U42(tt, 0, U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), 0), MARK(0)) A__U42(tt, x0, U12(x1)) -> c11(A__PLUS(U12(mark(x1)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U11(z0, z1))) -> c11(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U12(z0))) -> c11(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(isNat(z0))) -> c11(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U21(z0))) -> c11(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U31(z0, z1))) -> c11(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c11(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c11(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(plus(z0, z1))) -> c11(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(tt)) -> c11(A__PLUS(a__U12(tt), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(s(z0))) -> c11(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(0)) -> c11(A__PLUS(a__U12(0), mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2 ---------------------------------------- (217) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (218) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> mark(z0) a__U31(z0, z1) -> U31(z0, z1) a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U42(z0, z1, z2) -> U42(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), 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A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2))) A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0))) A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1))) A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1))) A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1))) A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1)))) A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0)))) A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0)))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1))) A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1))) A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1))) A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1))) A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1)))) A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0)))) A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0)))) A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0)))) A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1)))) A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1)))) A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt))) A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0)))) A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0))) A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2))) A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2))) A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2))) A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2))) A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2))) A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0))) A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3))) A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3))) A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3))) A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3))) A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2))) A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3))) A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3))) A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3))) A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3))) A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3))) A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0)))) A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1)))) A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2)))) A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2)))) A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2))) A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2))) A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2))) A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2))) A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2))) A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2))) A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0)))) A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0)))) A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1)))) A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2)))) A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2)))) A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1))) A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0)))) A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0)) A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0)))) A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0)) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1))) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1))) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U42(tt, U11(x0, z1), x2) -> c11(MARK(U11(x0, z1))) A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U42(tt, U12(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U42(tt, U12(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U42(tt, U12(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(U12(U21(z0)))) A__U42(tt, U12(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, U12(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(U12(plus(z0, z1)))) A__U42(tt, U12(tt), x1) -> c11(A__PLUS(mark(x1), a__U12(tt)), MARK(U12(tt))) A__U42(tt, U12(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U42(tt, U12(0), x1) -> c11(A__PLUS(mark(x1), a__U12(0)), MARK(U12(0))) A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0))) A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(isNat(plus(z0, z1)))) A__U42(tt, isNat(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(isNat(s(z0)))) A__U42(tt, isNat(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U42(tt, isNat(0), x1) -> c11(MARK(isNat(0))) A__U42(tt, isNat(z0), x1) -> c11(MARK(isNat(z0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(U21(U11(z0, z1)))) A__U42(tt, U21(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(U21(U12(z0)))) A__U42(tt, U21(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U42(tt, U21(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U42(tt, U21(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(U21(U31(z0, z1)))) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, U21(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(U21(plus(z0, z1)))) A__U42(tt, U21(tt), x1) -> c11(A__PLUS(mark(x1), a__U21(tt)), MARK(U21(tt))) A__U42(tt, U21(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U42(tt, U21(0), x1) -> c11(A__PLUS(mark(x1), a__U21(0)), MARK(U21(0))) A__U42(tt, U21(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0))) A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1))) A__U42(tt, U31(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1))) A__U42(tt, U31(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1))) A__U42(tt, U31(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(U31(U21(z0), x1))) A__U42(tt, U31(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1))) A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1))) A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(U31(U42(z0, z1, z2), x1))) A__U42(tt, U31(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(U31(plus(z0, z1), x1))) A__U42(tt, U31(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(U31(tt, x1))) A__U42(tt, U31(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1))) A__U42(tt, U31(x0, z1), x2) -> c11(MARK(U31(x0, z1))) A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1))) A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2))) A__U42(tt, U41(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2))) A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2))) A__U42(tt, U41(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(U41(U21(z0), x1, x2))) A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2))) A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2))) A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2))) A__U42(tt, U41(x0, z1, z2), x3) -> c11(MARK(U41(x0, z1, z2))) A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2))) A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(U42(U11(z0, z1), x1, x2))) A__U42(tt, U42(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(U42(U12(z0), x1, x2))) A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(U42(isNat(z0), x1, x2))) A__U42(tt, U42(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(U42(U21(z0), x1, x2))) A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(U42(U31(z0, z1), x1, x2))) A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U42(U41(z0, z1, z2), x1, x2))) A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U42(U42(z0, z1, z2), x1, x2))) A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U42(plus(z0, z1), x1, x2))) A__U42(tt, U42(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(U42(tt, x1, x2))) A__U42(tt, U42(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(U42(s(z0), x1, x2))) A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2))) A__U42(tt, U42(x0, z1, z2), x3) -> c11(MARK(U42(x0, z1, z2))) A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2))) A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U42(tt, plus(x0, U12(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(plus(x0, U12(z0)))) A__U42(tt, plus(x0, isNat(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U42(tt, plus(x0, U21(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(plus(x0, U21(z0)))) A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(plus(x0, U31(z0, z1)))) A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(plus(x0, U41(z0, z1, z2)))) A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(plus(x0, U42(z0, z1, z2)))) A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U42(tt, plus(x0, tt), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U42(tt, plus(x0, s(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U42(tt, plus(x0, 0), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U42(tt, plus(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U42(tt, plus(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(plus(U12(z0), x1))) A__U42(tt, plus(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U42(tt, plus(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(plus(U21(z0), x1))) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(plus(U31(z0, z1), x1))) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1))) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(plus(U42(z0, z1, z2), x1))) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), x2) -> c11(MARK(plus(x0, x1))) A__U42(tt, s(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(x1, z1)) -> c11(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U12(z0), x2)) -> c11(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(isNat(z0), x2)) -> c11(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U21(z0), x2)) -> c11(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(tt, x2)) -> c11(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(s(z0), x2)) -> c11(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(0, x2)) -> c11(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U42(tt, 0, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), 0)) A__U42(tt, s(z0), U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U12(x1)) -> c11(A__PLUS(U12(mark(x1)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U11(z0, z1))) -> c11(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U12(z0))) -> c11(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(isNat(z0))) -> c11(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U21(z0))) -> c11(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U31(z0, z1))) -> c11(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c11(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c11(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(plus(z0, z1))) -> c11(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(tt)) -> c11(A__PLUS(a__U12(tt), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(s(z0))) -> c11(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(0)) -> c11(A__PLUS(a__U12(0), mark(x0)), MARK(x0)) A__U42(tt, 0, U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), 0)) S tuples: A__U31(tt, z0) -> c6(MARK(z0)) MARK(isNat(z0)) -> c22(A__ISNAT(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) MARK(U12(z0)) -> c21(MARK(z0)) MARK(U21(z0)) -> c23(MARK(z0)) A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0)) A__U41(tt, x0, z0) -> c8(A__ISNAT(z0)) A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1)) A__U42(tt, tt, x1) -> c10(MARK(x1)) A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0)) A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0)) A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c17(A__U31(tt, 0)) A__PLUS(z0, 0) -> c17(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(tt, x1)) -> c20(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c20(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(tt, x1)) -> c24(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c24(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0))) MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2)) MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c27(MARK(x0)) MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0)) A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1))) A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1))) A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2)) A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2))) A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2))) A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2)) A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1))) A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1))) A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U42(tt, U12(x0), x1) -> c10(MARK(x1)) A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0)))) A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0)))) A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2))) A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2))) A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U42(tt, isNat(0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(z0), x1) -> c10(MARK(x1)) A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0))) A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0))) A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1)) A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2))) A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2))) A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U42(tt, U21(x0), x1) -> c10(MARK(x1)) A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0)))) A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0)))) A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) 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A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0)))) A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0)))) A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1)))) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2)))) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2)))) A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1)))) A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt))) A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0)))) A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0))) A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1))) A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0)))) A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1))) A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1))) A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1))) A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1))) A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1)))) A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0)))) A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0)))) A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0)))) A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1)))) A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2)))) A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2)))) A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1)))) A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt))) A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0)))) A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0))) A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1))) A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2))) A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2))) A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1))) A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2))) A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2))) A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2))) A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2))) A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2))) A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2))) A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2))) A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2))) A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2))) A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2))) A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2))) A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0))) A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3))) A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2))) A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3))) A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3))) A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3))) A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3))) A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3))) A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3))) A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3))) A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3))) A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3))) A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0))) A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3))) A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2))) A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3))) A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3))) A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3))) A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3))) A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3))) A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3))) A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3))) A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3))) A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3))) A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3))) A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0))) A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0)))) A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), 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plus(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U42(tt, plus(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(plus(U21(z0), x1))) A__U42(tt, plus(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(plus(U31(z0, z1), x1))) A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1))) A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(plus(U42(z0, z1, z2), x1))) A__U42(tt, plus(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U42(tt, plus(x0, x1), x2) -> c11(MARK(plus(x0, x1))) A__U42(tt, s(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U11(x1, z1)) -> c11(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U12(z0), x2)) -> c11(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(isNat(z0), x2)) -> c11(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U21(z0), x2)) -> c11(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(tt, x2)) -> c11(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(s(z0), x2)) -> c11(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U42(tt, x0, U11(0, x2)) -> c11(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U42(tt, 0, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), 0)) A__U42(tt, s(z0), U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U42(tt, x0, U12(x1)) -> c11(A__PLUS(U12(mark(x1)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U11(z0, z1))) -> c11(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U12(z0))) -> c11(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(isNat(z0))) -> c11(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U21(z0))) -> c11(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U31(z0, z1))) -> c11(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c11(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c11(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(plus(z0, z1))) -> c11(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(tt)) -> c11(A__PLUS(a__U12(tt), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(s(z0))) -> c11(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(x0)) A__U42(tt, x0, U12(0)) -> c11(A__PLUS(a__U12(0), mark(x0)), MARK(x0)) A__U42(tt, 0, U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), 0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2 Compound Symbols: c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2